1. Water waves at the surface of a pond pass a floating log of length L. The log is at rest relative

to the bank. The diagram shows wave crests at one instant.

L

The number of crests passing the log per unit time is N. The speed of the water waves relative

to the log at rest is

A. (N – 1).

7

L

B. (N – 1).

6

L

C. (N).

7

L

D. (N).

6

L

(1)

2. Two identical triangular pulses of amplitude X travel toward each other along a string. At the

instant shown on the diagram below, point M is midway between the two pulses.

X

X

M

1

The amplitude of the disturbance in the string as the pulses move through M is

A. 2X.

B. X.

C.

.2

X

D. 0.(1)

3. A person is walking along one side of a building and a car is driving along another side of the

building.

The person can hear the car approach but cannot see it. This is explained by the fact that sound

waves

A. travel more slowly than light waves.

B. are diffracted more at the corner of the building than light waves.

C. are refracted more at the corner of the building than light waves.

D. are longitudinal waves.(1)

2

4. A pulse is sent down a string fixed at one end.

Which one of the following diagrams best represents the reflected pulse?

A.

C.

B.

D.

(1)

5. This question is about waves and wave properties.

(a) By making reference to waves, distinguish between a ray and a wavefront.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(3)

3

The diagram below shows three wavefronts incident on a boundary between medium I and

medium R. Wavefront CD is shown crossing the boundary. Wavefront EF is incomplete.

medium I

medium R

A

B

C

D

E

F

(b) (i) On the diagram above, draw a line to complete the wavefront EF.(1)

(ii) Explain in which medium, I or R, the wave has the higher speed.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(3)

(iii) By taking appropriate measurements from the diagram, determine the ratio of the

speeds of the wave travelling from medium I to medium R.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(2)

4

The graph below shows the variation with time t of the velocity v of one particle of the medium

through which the wave is travelling.

8

6

4

2

0

–2

–4

–6

–8

0 1 2 3 4 5 6

t / ms

v / ms–1

7

(c) (i) Explain how it can be deduced from the graph that the particle is oscillating.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(2)

(ii) Determine the frequency of oscillation of the particle.

...........................................................................................................................

...........................................................................................................................(2)

(iii) Mark on the graph with the letter M one time at which the particle is at maximum

displacement.(1)

(iv) Estimate the area between the curve and the x-axis from the time t = 0 to the time

t = 1.5 ms.

...........................................................................................................................

...........................................................................................................................(2)

5

(v) Suggest what the area in c (iv) represents.

...........................................................................................................................(1)

(Total 17 marks)

6. A sound emitting source moves along a straight line with speed v relative to an observer at rest.

v

Observer

The speed of sound relative to the medium is c. The observer measures the speed of sound

emitted by the source as

A. c.

B. c + v.

C. c – v.

D. v – c.(1)

7. The diagram below shows ocean waves incident on a stone barrier protecting boats anchored

behind it.

Boats

Barrier

Waves

6

The boats could still be at risk of damage by waves mainly as a result of

A. refraction.

B. standing waves.

C. diffraction.

D. reflection.(1)

8. This question is about waves and wave properties.

The diagram below shows three wavefronts incident on a boundary between medium I and

medium R. Wavefront CD is shown crossing the boundary. Wavefront EF is incomplete.

medium I

medium R

A

B

C

D

E

F

(a) (i) On the diagram above, draw a line to complete the wavefront EF.(1)

7

(ii) Explain in which medium, I or R, the wave has the higher speed.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(3)

The graph below shows the variation with time t of the velocity v of one particle of the medium

through which the wave is travelling.

8

6

4

2

0

–2

–4

–6

–8

0 1 2 3 4 5 6

t / ms

v / ms–1

7

(b) (i) Explain how it can be deduced from the graph that the particle is oscillating.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(2)

(ii) Determine the frequency of oscillation of the particle.

...........................................................................................................................

...........................................................................................................................(2)

8

(iii) Mark on the graph with the letter M one time at which the particle is at maximum

displacement.(1)

(iv) Estimate the area between the curve and the x-axis from the time t = 0 to the time

t = 1.5 ms.

...........................................................................................................................

...........................................................................................................................(2)

(v) Suggest what the area in b (iv) represents.

...........................................................................................................................(1)

(c) (i) State the principle of superposition.

...........................................................................................................................

...........................................................................................................................(2)

Two loudspeakers S1 and S2 are connected to the same output of a frequency generator and are

placed in a large room as shown below.

S

S

2

1

560 cm

580 cm

550 cm

P

M

9

Sound waves of wavelength 40 cm and amplitude A are emitted by both loudspeakers.

M is a point distance 550 cm from both S1 and S2. Point P is a distance 560 cm from S1 and

580 cm from S2.

(ii) State and explain what happens to the loudness of the sound detected by a

microphone when the microphone is moved from point M to point P.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(4)

(iii) Referring to the diagram above, the amplitude of the wave emitted by S1 is now

increased to 2A. The wave emitted by S2 is unchanged. Deduce what change, if

any, occurs in the loudness of the sound at point M and at point P when this

change in amplitude is made.

at point M: ......................................................................................................

......................................................................................................

at point P: ......................................................................................................

......................................................................................................(4)

(iv) The loudspeakers are now replaced with two monochromatic light sources. State

the reason why bright and dark fringes are not observed along the line PM.

...........................................................................................................................(1)

Waves of frequency f and speed c are emitted by a stationary source of sound. An observer

moves along a straight line towards the source at a constant speed v.

10

(d) State, in terms of f, c and v, an expression for

(i) the wavelength of the sound detected by the observer.

...........................................................................................................................(1)

(ii) the apparent speed of the wave as measured by the observer.

...........................................................................................................................(1)

(Total 25 marks)

9. A plane wave approaches and passes through the boundary between two media. The speed of

the wave in medium 1 is greater than that in medium 2. Which one of the following diagrams

correctly shows the wavefronts?

A.

C.

B.

D.

Medium 1

Medium 1

Medium 1

Medium 1

Medium 2

Medium 2

Medium 2

Medium 2

(1)

11

10. Two particles X and Y are situated a distance

apart on a stationary wave of wavelength λ.λ2

1

The variation with time t of the displacement dx of X is shown below.

0

d

t0

X

Which one of the following correctly shows the variation with time t of the displacement dY of

particle Y?

0

0

0

0

d

d

d

d

t

t

t

t

0

0

0

0

A.

C.

B.

D.

Y

Y

Y

Y

(1)

12

11. This question is about sound waves.

A sound wave of frequency 660 Hz passes through air. The variation of particle displacement

with distance along the wave at one instant of time is shown below.

displacement / mm

0.5

0

–0.5

distance / m0 1.0 2.0

(a) State whether this wave is an example of a longitudinal or a transverse wave.

.....................................................................................................................................(1)

(b) Using data from the above graph, deduce for this sound wave,

(i) the wavelength.

...........................................................................................................................(1)

(ii) the amplitude.

...........................................................................................................................(1)

13

(iii) the speed.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(2)

(Total 5 marks)

12. The speed of a wave is defined as

A. the speed at which the particles of the wave vibrate.

B. the speed of the medium through which the wave passes.

C. the speed of transfer of the energy of the wave.

D. the speed at which the vibrations of the wave are produced.(1)

14

13. Which diagram best shows diffraction of plane wavefronts at a single slit?

A.

C.

B.

D.

(1)

14. A source of sound moves directly towards a stationary observer. The frequency of the sound

detected by the observer is different from the source frequency because

A. the loudness of the sound increases as the source moves towards the observer.

B. the apparent wavelength of the sound is longer.

C. the speed of sound relative to the observer is increased.

D. the apparent wavelength of the sound is shorter.(1)

15

15. This question is about atomic and nuclear structure and fundamental forces.

In a nuclear model of the atom, most of the atom is regarded as empty space. A tiny nucleus is

surrounded by a number of electrons.

(a) Outline one piece of experimental evidence that supports this nuclear model of the atom.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(3)

(b) Explain why the protons in a nucleus do not fly apart from each other.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(2)

16

(c) In total, there are approximately 1029 electrons in the atoms making up a person.

Estimate the electrostatic force of repulsion between two people standing 100 m apart as

a result of these electrons.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(4)

(d) Estimate the gravitational force of attraction between two people standing 100 m apart.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(2)

(e) Explain why two people standing 100 m apart would not feel either of the forces that you

have calculated in parts (c) and (d).

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(2)

(Total 13 marks)

17

16. This question is about sound waves.

In order to demonstrate two-source interference of sound waves, two loudspeakers are

connected to the same output of a signal generator. The loudspeakers are fixed 4.0 m apart.

In the diagram below, the line AB is parallel to the loudspeakers and at a distance of 10.0 m

from the loudspeakers. Point P is midway between the loudspeakers.

signalgenerator

P (loud)

Q (quiet)

R (loud)

10.0 m

4.0 m

A

B

Katerina walks along the line AB carrying a microphone connected to a detector. She registers

a sound that alternates in intensity from loud to quiet.

(a) Describe the conditions necessary for a sound of minimum intensity to be registered at Q.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(3)

18

As Katerina runs along the line AB she counts the number of loud sounds registered in a given

time. The frequency of the sound emitted by both loudspeakers is 360 Hz and the speed of

sound in air is 330 ms–1.

(b) Estimate the speed at which she is running if the maximum sounds occur with a

frequency of about 2 Hz.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(6)

(Total 9 marks)

17. The diagram shows the variation with distance x along a wave with its displacement d.

The wave is travelling in the direction shown.

d

x

direction of travel

19

The period of the wave is T. Which one of the following diagrams shows the displacement of

the wave at later?

4

T

d

d

d

d

x

x

x

x

A.

C.

B.

D.

(1)

18. When a wave crosses the boundary between two media, which one of the following properties

of the wave does not change?

A. Amplitude

B. Wavelength

C. Frequency

D. Speed(1)

20

19. A pipe, open at both ends, has a length L. The speed of sound in the air in the pipe is v. The

frequency of vibration of the fundamental (first harmonic) standing wave that can be set up in

the pipe is

A.

.L

v

2

B. .

v

L

2

C. .

L

v4

D. .

v

L

4

(1)

20. Jeremy is walking alongside a building and is approaching a road junction. A fire engine is

sounding its siren and approaching the road along which Jeremy is walking.

Jeremy

Fire engineBuilding

Jeremy cannot see the fire engine but he can hear the siren. This is due mainly to

A. reflection.

B. refraction.

C. the Doppler effect.

D. diffraction.(1)

21

21. This question is about waves and wave motion.

(a) (i) Define what is meant by the speed of a wave.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(2)

(ii) Light is emitted from a candle flame. Explain why, in this situation, it is correct to

refer to the “speed of the emitted light”, rather than its velocity.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(2)

(b) (i) Define, by reference to wave motion, what is meant by displacement.

...........................................................................................................................

...........................................................................................................................(2)

(ii) By reference to displacement, describe the difference between a longitudinal wave

and a transverse wave.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(3)

22

The centre of an earthquake produces both longitudinal waves (P waves) and transverse waves

(S waves). The graph below shows the variation with time t of the distance d moved by the two

types of wave.

d / km

t / s

P wave S wave

1200

800

400

0

0 25 50 75 100 125 150 175 200 225

(c) Use the graph to determine the speed of

(i) the P waves.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(1)

(ii) the S waves.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(1)

23

The waves from an earthquake close to the Earth’s surface are detected at three laboratories L1,

L2 and L3. The laboratories are at the corners of a triangle so that each is separated from the

others by a distance of 900 km, as shown in the diagram below.

L L

L

1 2

3

900 km

The records of the variation with time of the vibrations produced by the earthquake as detected

at the three laboratories are shown below. All three records were started at the same time.

time

start of trace

L

L

L

1

2

3

On each record, one pulse is made by the S wave and the other by the P wave. The separation

of the two pulses is referred to as the S-P interval.

(d) (i) On the trace produced by laboratory L2, identify, by reference to your answers in

(c), the pulse due to the P wave (label the pulse P).(1)

(ii) Using evidence from the records of the earthquake, state which laboratory was

closest to the site of the earthquake.

...........................................................................................................................(1)

24

(iii) State three separate pieces of evidence for your statement in (d)(ii).(3)

1. .................................................................................................................

.................................................................................................................

2. .................................................................................................................

.................................................................................................................

3. .................................................................................................................

.................................................................................................................

(iv) The S-P intervals are 68 s, 42 s and 27 s for laboratories L1, L2 and L3

respectively. Use the graph, or otherwise, to determine the distance of the

earthquake from each laboratory. Explain your working.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

Distance from L1 = ......................km

...........................................................................................................................

Distance from L2 = ......................km

...........................................................................................................................

Distance from L3 = ......................km

...........................................................................................................................(4)

(v) Mark on the diagram a possible site of the earthquake.(1)

25

There is a tall building near to the site of the earthquake, as illustrated below.

building

ground

direction of vibrations

The base of the building vibrates horizontally due to the earthquake.

(e) (i) On the diagram above, draw the fundamental mode of vibration of the building

caused by these vibrations.(1)

The building is of height 280 m and the mean speed of waves in the structure of the building is

3.4 × 103 ms–1.

(ii) Explain quantitatively why earthquake waves of frequency about 6 Hz are likely to

be very destructive.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(3)

(Total 25 marks)

26

22. Two lamps producing light of the same colour are placed close to one another. A two source

interference pattern is not observed because

A. the lamps do not emit light of a single frequency.

B. the phase difference between the light from the lamps is continually changing.

C. the intensity of the light emitted by the lamps is not the same.

D. the two lamps are not exact point sources.(1)

23. This question is about earthquake waves.

(a) (i) Light is emitted from a candle flame. Explain why, in this situation, it is correct to

refer to the “speed of the emitted light”, rather than its velocity.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(2)

(ii) By reference to displacement, describe the difference between a longitudinal wave

and a transverse wave.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(3)

27

The centre of an earthquake produces both longitudinal waves (P waves) and transverse waves

(S waves). The graph below shows the variation with time t of the distance d moved by the two

types of wave.

d / km

t / s

P wave S wave

1200

800

400

0

0 25 50 75 100 125 150 175 200 225

(b) Use the graph to determine the speed of

(i) the P waves.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(1)

(ii) the S waves.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(1)

28

The waves from an earthquake close to the Earth’s surface are detected at three laboratories L1,

L2 and L3. The laboratories are at the corners of a triangle so that each is separated from the

others by a distance of 900 km, as shown in the diagram below.

L L

L

1 2

3

900 km

The records of the variation with time of the vibrations produced by the earthquake as detected

at the three laboratories are shown below. All three records were started at the same time.

time

start of trace

L

L

L

1

2

3

On each record, one pulse is made by the S wave and the other by the P wave. The separation

of the two pulses is referred to as the S-P interval.

(c) (i) On the trace produced by laboratory L2, identify, by reference to your answers in

(b), the pulse due to the P wave (label the pulse P).(1)

(ii) Using evidence from the records of the earthquake, state which laboratory was

closest to the site of the earthquake.

...........................................................................................................................(1)

29

(iii) State three separate pieces of evidence for your statement in (c)(ii).

1 .................................................................................................................

.................................................................................................................

2 .................................................................................................................

.................................................................................................................

3 .................................................................................................................

.................................................................................................................(3)

(iv) The S-P intervals are 68 s, 42 s and 27 s for laboratories L1, L2 and L3

respectively. Use the graph, or otherwise, to determine the distance of the

earthquake from each laboratory. Explain your working.

Distance from L1 = ......................km

...........................................................................................................................

Distance from L2 = ......................km

...........................................................................................................................

Distance from L3 = ......................km

...........................................................................................................................(4)

(v) Mark on the diagram a possible site of the earthquake.(1)

30

There is a tall building near to the site of the earthquake, as illustrated below.

building

ground

direction of vibrations

The base of the building vibrates horizontally due to the earthquake.

(d) (i) On the diagram, draw the fundamental mode of vibration of the building caused by

these vibrations.(1)

The building is of height 280 m and the mean speed of waves in the structure of the building is

3.4 × 103 ms–1.

(ii) Explain quantitatively why earthquake waves of frequency about 6 Hz are likely to

be very destructive.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(3)

(Total 21 marks)

31

24. This question is about the Doppler effect.

The diagram below shows wavefronts produced by a stationary wave source S. The spacing of

the wavefronts is equal to the wavelength of the waves. The wavefronts travel with speed V.

S

(a) The source S now moves to the right with speed

V. In the space below, draw four2

1

successive wavefronts to show the pattern of waves produced by the moving source.

(3)

32

(b) Derive the Doppler formula for the observed frequency f0 of a sound source, as heard by

a stationary observer, when the source approaches the stationary observer with speed v.

The speed of sound is V and the frequency of the sound emitted by the source is f.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(3)

The Sun rotates about its centre. The light from one edge of the Sun, as seen by a stationary

observer, shows a Doppler shift of 0.004 nm for light of wavelength 600.000 nm.

(c) Assuming that the Doppler formula for sound may be used for light, estimate the linear

speed of a point on the surface of the Sun due to its rotation.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(3)

(Total 9 marks)

33

25. On which one of the following graphs is the wavelength λ and the amplitude a of a wave

correctly represented?

Displacement

Displacement

Displacement

Displacement

0

0

0

0

0

0

0

0

a

a

a

a

λ

λ

λ

λ

Distance alongwave

Distance alongwave

Distance alongwave

Distance alongwave

A.

B.

C.

D.

(1)

34

26. Standing waves in an open pipe come about as a result of

A. reflection and superposition.

B. reflection and diffraction.

C. superposition and diffraction.

D. reflection and refraction.(1)

27. The diagram below shows two wave pulses moving towards one another.

Which one of the following diagrams shows the resultant pulse when the two pulses are

superposed?

A. B.

C. D.

(1)

35

28. A source of sound emits waves of wavelength λ, period T and speed v when at rest. The source

moves away from a stationary observer at speed V, relative to the observer. The wavelength of

the sound waves, as measured by the observer is

A. λ + vT.

B. λ – vT.

C. λ +VT.

D. λ – VT.(1)

29. This question is about the interference of waves.

(a) State the principle of superposition.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(2)

36

A wire is stretched between two points A and B.

A B

A standing wave is set up in the wire. This wave can be thought of as being made up from the

superposition of two waves, a wave X travelling from A to B and a wave Y travelling from B to

A. At one particular instant in time, the displacement of the wire is as shown. A background

grid is given for reference and the equilibrium position of the wire is shown as a dotted line.

A B

37

(b) On the grids below, draw the displacement of the wire due to wave X and wave Y.

A

A

B

B

Wave X

Wave Y

(4)

38

The diagram below shows an arrangement (not to scale) for observing the interference pattern

produced by the superposition of two light waves.

single slit

double slit

monochromaticlight source

Screen

S

S

S

1

2

P

O

S1 and S2 are two very narrow slits. The single slit S ensures that the light leaving the slits S1

and S2 is coherent.

(c) (i) Define coherent.

...........................................................................................................................

...........................................................................................................................(1)

(ii) Explain why the slits S1 and S2 need to be very narrow.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(2)

(Total 9 marks)

39

30. What change, if any, occurs in the wavelength and frequency of a light wave as it crosses a

boundary from air into glass?

Wavelength Frequency

A. Decreases Decreases

B. Decreases Unchanged

C. Increases Increases

D. Increases Unchanged

(1)

31. The variation with time t of the separate displacements d of a point in a medium due to two

waves is shown below.

+2a

+a

+a

0

0

–a

–a

–2a

d

d

t

t

40

The waves are superposed. Which of the following diagrams shows the variation with time t of

the resultant displacement d of the point in the medium?

+2a +2a

+3a +3a

+a +a

+a+a

0 0

00

–a –a

–a–a

–2a –2a

–3a –3a

d d

dd

t t

tt

A. B.

C. D.

(1)

41

32. Which of the following diagrams best illustrates the diffraction of waves by an obstacle?

A.

C.

B.

D.

(1)

42

33. A source S produces sound waves of frequency f and is moving along a straight line as shown

below.

I

II III

IVS

Which observer I, II, III or IV could hear a sound of frequency f when the source is in the

position shown?

A. I

B. II

C. III

D. IV(1)

34. In order that the interference between the waves emitted by two light sources can be observed,

it is essential that the sources must emit waves that

A. have the same amplitude.

B. are in phase.

C. have the same colour.

D. have a constant phase difference between them.(1)

43

35. This question is about wave properties and interference.

The diagram below represents the direction of oscillation of a disturbance that gives rise to a

wave.

(a) By redrawing the diagram in the spaces below, add arrows to show the direction of wave

energy transfer to illustrate the difference between

(i) a transverse wave and

(1)

(ii) a longitudinal wave.

(1)

44

A wave travels along a stretched string. The diagram below shows the variation with distance

along the string of the displacement of the string at a particular instant in time. A small marker

is attached to the string at the point labelled M. The undisturbed position of the string is shown

as a dotted line.

Directions of wave travel

M

(b) On the diagram above

(i) draw an arrow to indicate the direction in which the marker is moving.(1)

(ii) indicate, with the letter A, the amplitude of the wave.(1)

(iii) indicate, with the letter λ, the wavelength of the wave.(1)

(iv) draw the displacement of the string a time later, where T is the period of

4

T

oscillation of the wave. Indicate, with the letter N, the new position of the marker.(2)

The wavelength of the wave is 5.0 cm and its speed is 10 cm s–1.

(c) Determine

(i) the frequency of the wave.

...........................................................................................................................(1)

45

(ii) how far the wave has moved in s.

4

T

(2)

Interference of waves

(d) By reference to the principle of superposition, explain what is meant by constructive

interference.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(4)

(Total 14 marks)

36. The wavelength of a progressive transverse wave is defined as

A. the distance between a crest and its neighbouring trough.

B. the distance between any two crests of the wave.

C. the distance moved by a wavefront during one oscillation of the source.

D. the distance moved by a particle in the wave during one oscillation of the source.(1)

46

37. The two graphs show the variation with time of the individual displacements of two waves as

they pass through the same point.

A

A

–A

–A

x

–x

1

2

1

2

1

2

0

0

0

0

T

T

time

time

displacement

displacement

The displacement of the resultant wave at the point at time T is equal to

A. x1 + x2.

B. x1 – x2.

C. A1 + A2.

D. A1 – A2.

(1)

47

38. This question is about waves and wave motion.

(a) Describe, by reference to the propagation of energy, what is meant by a transverse wave.

Transverse wave

(2)

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

(b) State one example, other than a wave on a string, of a transverse wave.

.....................................................................................................................................(1)

A transverse wave is travelling along a string that is under tension. The diagram below shows

the displacement of part of the string at time t = 0. The dotted line shows the position of the

string when there is no wave travelling along it.

distance along string / cm5.0 15 25 35 45

displacement / cm

48

(c) On the diagram above, draw lines to identify for this wave

(i) the amplitude (label this A);(1)

(ii) the wavelength (label this λ).(1)

(d) The period of the wave is 1.2 × 10–3 s. Deduce that the speed of the wave is 250 m s–1.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(2)

(e) Using the axes below, draw the displacement of the string when t = 3.0 × 10–4 s. (The

displacement of the string at t = 0 is shown as a dotted line.)

distance along string / cm5.0 15 25 35 45

displacement / cm

(3)

(Total 10 marks)

49

39. Graph P shows how the displacement at one point in a wave varies with time.

Graph Q shows how the displacement in the same wave varies with distance along the wave at

one particular time.

0

0

t

x x

t

x

0

0

displacement

displacement

2

2 3

1

1

time

distance

Graph P

Graph Q

50

Which one of the following expressions gives the speed of the wave?

A.

1

1

t

x

B.

2

2

t

x

C.

( )( )

12

12

tt

xx

−

−

D.

( )( )

12

13

tt

xx

−

−

(1)

40. A string is stretched between two fixed points. The string is plucked at its centre and is seen to

vibrate with frequency f as shown below.

Which one of the following expressions gives the frequencies of other possible modes of

vibration that have an antinode at the centre? The number n in each expression is an integer.

A. nf

B. (2n – 1)f

C. (n – 1)f

D. (n + 1)f

(1)

51

41. Which one of the following diagrams best represents wavefronts produced by a source of sound

of constant frequency as it moves at constant speed towards a stationary observer at O?

O

O

O

O

A.

C.

B.

D.

(1)

42. The waves from two light sources meet at a point. Which condition is essential for interference

to be observed?

A. Constant phase difference between the waves

B. Equal amplitude of the waves

C. Equal frequency of the waves

D. Equal intensities of the waves

(1)

52

43. Light from a double slit arrangement produces bright and dark fringes on a screen in the region

near point P, as indicated below.

P

screendouble slit

not to scale

coherentlight

The light from the two slits has equal amplitudes on reaching point P.

Which one of the following gives the change, if any, in the appearance of the bright and the

dark fringes when the amplitude of the light wave from one slit is reduced?

Bright fringes Dark fringes

A. Remains the same Remains the same

B. Becomes less bright Remains the same

C. Becomes less bright Becomes more bright

D. Remains the same Becomes more bright

(1)

44. The graph below shows the variation of air pressure with distance along a wave at one given

time. The arrow indicates the direction of travel of the wave.

air pressure

+

normal air pressure

–

P

distance along wave

53

The air pressure at point P is

A. increasing.

B. decreasing.

C. constant.

D. zero.(1)

45. Sound waves move faster in warm air than in cold air. The diagram below shows plane waves

in cold air moving towards a boundary with warm air.

warm air

cold air boundary

I

II

III

IV

Which of the arrows shows the possible direction of waves after reaching the boundary?

A. I

B. II

C. III

D. IV(1)

54

46. The speed of sound in still air is c. A source of sound moves away from an observer at speed v.

What will be the speed of sound as measured by the observer?

A. c

B. c + v

C. c – v

D. v – c(1)

47. For a standing wave, all the particles between two successive nodes have the same

A. amplitude only.

B. frequency only.

C. amplitude and frequency.

D. frequency and energy.(1)

55

48. The diagram below shows two pulses on a string travelling toward each other.

Which of the following diagrams best shows the shape of the string after the pulses have passed

through each other?

A.

B.

C.

D.

(1)

49. Two identical sources in a ripple tank generate waves of wavelength λ. The interfering waves

produce the wave pattern shown below.

I

II

III

IV

56

Along which of the labelled lines is the path difference between the waves from the sources

equal to 1.5 λ?

A. I

B. II

C. III

D. IV(1)

50. This question is about waves and wave properties.

(a) (i) Describe what is meant by a continuous travelling wave.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(2)

(ii) With reference to your answer in (a)(i), state what is meant by the speed of a

travelling wave.

...........................................................................................................................

...........................................................................................................................(1)

(b) Define, for a wave,

(i) frequency;

...........................................................................................................................

...........................................................................................................................(1)

57

(ii) wavelength.

...........................................................................................................................

...........................................................................................................................(1)

A tube that is open at both ends is placed in a deep tank of water, as shown below.

tuning fork, frequency 256 Hz

tube

tank of water

A tuning fork of frequency 256 Hz is sounded continuously above the tube. The tube is slowly

raised out of the water and, at one position of the tube, a maximum loudness of sound is heard.

(c) (i) Explain the formation of a standing wave in the tube.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(2)

58

(ii) The tube is raised a further small distance. Explain, by reference to resonance, why

the loudness of the sound changes.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(4)

(iii) The tube is gradually raised from a position of maximum loudness until the next

position of maximum loudness is reached. The length of the tube above the water

surface is increased by 65.0 cm. Calculate the speed of sound in the tube.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(2)

59

A sound wave is incident on the ear of a person. The pressure variation of the sound wave

causes a force F to be exerted on a moveable part of the ear called the eardrum. The variation

of the displacement x of the eardrum caused by the force F is shown below.

8

4

0

–4

–8

–2.0 –1.0 1.0 2.00

x/×10 mm–2

–5F/×10 N

(d) The eardrum has an area of 30 mm2. Calculate the pressure, in pascal, exerted on the

eardrum for a displacement x of 1.0 × 10–2 mm.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(2)

(e) (i) Calculate the energy required to cause the displacement to change from x = 0 to

x = +1.5 × 10–2 mm.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

60

(3)

The sound wave causing a maximum displacement of the eardrum of 1.5 × 10–2 mm has

frequency 1000 Hz.

(ii) Deduce that the energy causing the displacement in (e)(i) is delivered in a time of

0.25 ms. Also, determine the mean power of the sound wave to cause this

displacement.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(4)

(iii) Suggest the form of energy into which the energy of the sound wave has been

transformed at the eardrum.

...........................................................................................................................(1)

In an experiment to measure the speed of sound, two coherent sources S1 and S2 produce sound

waves of frequency 1700 Hz. A sound detector is moved along a line AB, parallel to S1S2 as

shown below.

S

S

1

2

B

X

P

A

61

When the detector is at P, such that S1P = S2P, maximum loudness of sound is detected. As the

detector is moved along AB, regions of minimum and maximum loudness are detected. Point X

is the third position of minimum loudness from P. The distance (S2X – S1X) is 0.50 m.

(f) (i) Determine the speed of the sound.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(3)

(ii) At X, no sound is detected. The loudness of the sound produced by S1 alone is

then reduced. State and explain the effect of this change on the loudness of sound

heard at X and at P.

at X: ...........................................................................................................

...........................................................................................................

...........................................................................................................

at P: ...........................................................................................................

...........................................................................................................

...........................................................................................................(4)

(Total 30 marks)

62

51. Diagram 1 below shows the displacement of part of a medium through which a wave is

travelling at time t = 0. Diagram 2 shows the displacement at a later time t = 4.0 s in which the

wave has moved forward 10 cm. In this time, the point P on the wave has moved from a crest

through zero displacement to a trough.

Diagram 1 Diagram 2

P

P

The wavelength of the wave is

A. 5.0 cm.

B. 10 cm.

C. 20 cm.

D. 40 cm.(1)

63

52. The diagram below shows a pulse travelling along a rope from X to Y. The end Y of the rope is

tied to a fixed support.

X

Y

When the pulse reaches end Y it will

A. disappear.

B. cause the end of the rope at Y to oscillate up and down.

C. be reflected and be inverted.

D. be reflected and not be inverted.(1)

53. Which one of the following is correct for transfer of energy along a standing wave and for

amplitude of vibration of the standing wave?

Transfer of energy along

a standing wave

Amplitude of vibration of

the standing wave

A. None Constant amplitude

B. None Variable amplitude

C. Energy is transferred Constant amplitude

D. Energy is transferred Variable amplitude

(1)

64

54. Two pipes P and Q are of the same length. Pipe P is closed at one end and pipe Q is open at

both ends. The fundamental frequency (first harmonic) of the closed pipe P is 220 Hz.

The best estimate for the fundamental frequency of the open pipe Q is

A. 880 Hz.

B. 440 Hz.

C. 110 Hz.

D. 55 Hz.(1)

55. In order that the light from two sources produces an observable interference pattern, it is

necessary that

A. the sources must be point sources.

B. the light emitted by the sources must be monochromatic.

C. the light from each source must be of the same intensity.

D. the light from the sources must be coherent.(1)

65

56. The properties of sound waves

Reflection and Refraction

One method of finding the position of fish beneath a boat is to send out a pulse of sound waves

from the bottom of a boat and time how long the pulse takes to return as shown below. The

speed of sound waves in water is 1500 m s–1.

water

emitter and receiver

fish

(a) The time between the pulse leaving the emitter and returning to the receiver is 12 ms.

Calculate the distance from the bottom of the boat to the fish.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................(2)

In order to find fish using this method, the effects of diffraction at the fish need to be

minimized.

(b) (i) The diagram below shows plane wavefronts incident on an obstacle. Complete the

diagram to show what is meant by diffraction of the wavefronts.

direction of

movement of

wavefronts

(2)

66

(ii) Explain why you would expect the effects of diffraction to be negligible when

sound of frequency 60 kHz is incident on a large fish.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(2)

The Doppler effect can be used to determine the speed of an object.

(c) (i) Explain what is meant by the Doppler effect.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(2)

(ii) A train approaches and then passes by a stationary observer. The train is moving

with constant velocity and emits a sound of constant frequency. The observer hears

the frequency change from 490 Hz to 410 Hz. The speed of sound in air is 340

m s–1. Estimate the speed of the train.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(4)

(Total 12 marks)

67

57. This question is about resolution.

(a) State the Rayleigh criterion for the images of two point sources to be just resolved.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................(2)

A man is walking along a straight path at night towards two light sources as shown below.

light

sources

path man

not drawn to scale

When the man is 150 m from the sources, the images of the two sources are just resolved by his

eye. The wavelength of the light from each source is 590 nm and the diameter of the aperture of

his eye is 5.0 mm.

(b) Estimate the distance between the two sources.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................(3)

(Total 5 marks)

68

58. A source produces water waves of frequency 10 Hz. The graph shows the variation with

horizontal position of the vertical displacement of the surface of water at one instant in time.

vertical displacement / cm0.4

0

–0.4

0 1.0 4.03.02.0 horizontal position / cm

The speed of the water waves is

A. 0.20 cm s−1.

B. 4.0 cm s−1.

C. 10 cm s−1.

D. 20 cm s−1.(1)

59. A wave travels from one medium to another. Which of the following is true about its frequency

and wavelength?

Frequency Wavelength

A. No change No change

B. Change No change

C. No change Change

D. Change Change

(1)

69

60. A bat approaches an insect of wing span length d. The bat emits a sound wave. The bat detects

the insect if the sound is reflected from the insect.

d

refected waves incident waves

The insect will not be located if

A. the insect’s speed is less than the speed of the sound wave.

B. the insect’s wing beat frequency is greater than the frequency of the sound wave.

C. the length d is much greater than the wavelength of the sound wave.

D. the length d is much smaller than the wavelength of the sound wave.(1)

61. Waves

(a) Distinguish, in terms of the propagation of energy, the difference between a transverse

travelling wave and a longitudinal travelling wave.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................(3)

70

(b) The diagram below shows an aluminium rod AB of length 1.50 m hanging horizontally

from two strings.

hammer

string string

A B

aluminium rod

1.50 m

End A of the rod is hit gently with a hammer. As a result, a wave pulse travels down the

rod and is reflected from end B. The hammer remains in contact with the rod until the

pulse reflected from end B reaches A. This pulse causes the hammer to rebound from the

end of the rod.

(i) Suggest, giving a reason , whether the wave pulse is longitudinal or transverse.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(2)

(ii) The hammer is in contact with end A of the rod for 6.00 × 10–4 s. Calculate the

speed of the pulse in the rod.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(2)

71

(iii) As a result of the rod being hit with the hammer, a sound is heard. Suggest how

this sound arises.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(3)

(Total 10 marks)

62. Monochromatic light crosses the boundary between two media. Which of the following

quantities is always the same for the light in both media?

A. Amplitude

B. Frequency

C. Speed

D. Wavelength(1)

The insect will not be located if

A. the insect’s speed is less than the speed of the sound wave.

B. the insect’s wing beat frequency is greater than the frequency of the sound wave.

C. the length d is much greater than the wavelength of the sound wave.

D. the length d is much smaller than the wavelength of the sound wave.(1)

72

63. A point source is moving at a constant speed in a straight-line towards the right and emits sound

waves of constant frequency. The speed of the source is less than the speed of sound. Which of

the diagrams correctly shows the wavefronts emitted by the source?

A. B.

C. D.

(1)

73

64. The diagram below shows the arrangement for a Young’s double slit experiment.

monochromatic light source

single slit double slit

S1

S

S2

The function of the single slit is

A. to direct the light towards S1 and S2.

B. to ensure equal intensities of light at S1 and S2.

C. to produce coherent light at S1 and S2.

D. to reduce the intensity of light at S1 and S2.

(1)

65. This question is about sound waves

Production of sound waves

(a) Distinguish, in terms of the propagation of energy, the difference between a transverse

travelling wave and a longitudinal travelling wave.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................(3)

74

(b) The diagram below shows an aluminium rod AB of length 1.50 m hanging horizontally

from two strings.

hammer

string string

A B

aluminium rod

1.50 m

End A of the rod is hit gently with a hammer. As a result, a wave pulse travels down the

rod and is reflected from end B. The hammer remains in contact with the rod until the

pulse reflected from end B reaches A. This pulse causes the hammer to rebound from the

end of the rod.

(i) Suggest, giving a reason, whether the wave pulse is longitudinal or transverse.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(2)

(ii) The hammer is in contact with end A of the rod for 6.00 × 10–4 s. Calculate the

speed of the pulse in the rod.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(2)

75

(iii) As a result of the rod being hit with the hammer, a sound is heard. Suggest how

this sound arises.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(3)

(iv) The sound produced in the air consists of waves of many different frequencies and

intensities. The loudest sound corresponds to a wave of frequency 1.67 × 103 Hz.

Deduce that this frequency is due to the rod vibrating in its fundamental (first

harmonic) mode.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(3)

Interference of sound waves

(c) In the diagram below, S1 and S2 are two small loudspeakers. They are connected to the

same sound source such that they emit sound waves of the same intensity and

wavelength. An instrument for detecting sound intensity is placed at point P such that

S1P = S2P.

X

S1

P

S2

The speaker S1 is moved slowly away from P along the line PS1. As S1 is moved, the

sound detected at P decreases and increases in intensity.

76

(i) Explain this observation.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(3)

(ii) In moving the source from S1 to point X, the intensity of the sound at P changes

from a maximum to a minimum. The distance S1X = 0.082 m.

Calculate the value of the wavelength of the sound emitted by the sources.

.........................................................................................................................(2)

(iii) S1 remains at the point X and the frequency f of the sound emitted from both S1

and S2 is changed until a maximum of sound intensity is detected at P. This occurs

when f = 4100 Hz.

Estimate a value for the speed of sound.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(2)

(Total 20 marks)

77

66. The diagram below shows a transverse wave on a string. The wave is moving from right to left.

X

Y

direction of wave

upwards

left right

downwards

In the position shown, point X has zero displacement and point Y is at a position of maximum

displacement. Which one of the following gives the subsequent direction of motion of point X

and of point Y?

Point X Point Y

A. left left

B. upwards upwards

C. downwards left

D. downwards upwards

(1)

78

67. Light is incident on an air-glass boundary as shown below.

PQ

air

R glassS

Which one of the following is a correct statement of Snell’s law?

A. sin P = constant × sin R

B. sin P = constant × sin S

C. sin Q = constant × sin R

D. sin Q = constant × sin S(1)

79

68. This question is about waves.

(a) In the scale diagram below, plane wavefronts travel from medium 1 to medium 2 across

the boundary AB.

direction of travel

medium 1

A B

medium 2

State and explain in which medium the wavefronts have the greater speed.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................(3)

(b) By taking measurements from the diagram, determine the ratio

.2mediuminwaveofspeed

1mediuminwaveofspeed

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................(3)

(Total 6 marks)

80

69. Which one of the following correctly describes the change, if any, in the speed, wavelength and

frequency of a light wave as it passes from air into glass?

Speed Wavelength Frequency

A. decreases decreases unchanged

B. decreases unchanged decreases

C. unchanged increases decreases

D. increases increases unchanged

(1)

70. A tube is filled with water and a vibrating tuning fork is held above its open end.

x

y

tuning fork

water

tap

The tap at the base of the tube is opened. As the water runs out, the sound is loudest when the

water level is a distance x below the top of the tube. A second loud sound is heard when the

water level is a distance y below the top. Which one of the following is a correct expression for

the wavelength λ of the sound produced by the tuning fork?

A. λ = y

B. λ = 2x

C. λ = y − x

D. λ = 2(y − x)(1)

81

82

71. A source S, moving at constant speed, emits a sound of constant frequency. The source passes

by a stationary observer O, as shown below.

S

O

Which one of the following shows the variation with time t of the frequency f observed at O as

the source S approaches and passes by the observer.

A.f

0 0 t

B.f

0 0 t

C.f

0 0 t

D.f

0 0 t

(1)

83

72. Water waves of wavelength 2.0 m are produced by two sources S1 and S2. The sources vibrate

in phase.

S1

S2

1 m3 m

P

Point P is 1 m from S1 and 3 m from S2. S1 alone and S2 alone each produce a wave of

amplitude a at P. Which one of the following is the amplitude of the resultant wave at point P

when S1 and S2 are both emitting waves?

A. 2a

B. a

C. a

2

1

D. Zero(1)

73. This question is about waves and wave properties.

Travelling and standing (stationary) waves

(a) State two differences between a travelling wave and a standing (stationary) wave.

1. .........................................................................................................................

.........................................................................................................................

2. .........................................................................................................................

.........................................................................................................................(2)

84

(b) In the scale diagram below, plane wavefronts travel from medium 1 to medium 2 across

the boundary AB.

direction of travel

medium 1

A B

medium 2

State and explain in which medium the wavefronts have the greater speed.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................(3)

(c) By taking measurements from the diagram, determine the ratio

.2mediuminwaveofspeed

1mediuminwaveofspeed

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................(3)

85

(d) To demonstrate the production of a standing wave, Samantha attaches the end B of a

length AB of rubber tubing to a rigid support. She holds the other end A of the tubing,

pulls on it slightly and then shakes the end A in a direction at right angles to AB. At a

certain frequency of shaking, the tubing is seen to form the standing wave pattern shown

below.

A B

Explain how this pattern is formed.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................(5)

86

(e) The speed v with which energy is propagated in the tubing by a travelling wave depends

on the tension T in the tubing. The relationship between these quantities is

Tkv=

where k is a constant.

In an experiment to verify this relationship, the fundamental (first harmonic) frequency f

was measured for different values of tension T.

(i) Explain how the results of this experiment, represented graphically, can be used to

verify the relationship

.Tkv=

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(4)

(ii) In the experiment, the length of the tubing was kept constant at 2.4 m. The

fundamental frequency for a tension of 9.0 N in the tubing was 1.8 Hz. Calculate

the numerical value of the constant k.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(3)

87

The Doppler effect

(f) A source S emits sound waves at constant frequency. In the diagram below, S is moving

at constant speed in the direction shown, along a straight-line between two stationary

observers A and B.

B A

S

(i) Draw, on the above diagram, three wavefronts representing the waves emitted by S.(2)

(ii) Use your sketch to explain any difference in the frequency of the sound as heard

by observer A and by observer B.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(2)

(Total 24 marks)

88

74. A string is held horizontally with one end attached to a fixed support. Two pulses are created at

the free end of the string. The pulses are moving towards the fixed support as shown in the

diagram below.

string

fixed support

Which one of the following diagrams is a possible subsequent picture of the string?

A. B.

C. D.

(1)

75. A water surface wave (ripple) is travelling to the right on the surface of a lake. The wave has

period T. The diagram below shows the surface of the lake at a particular instant of time. A

piece of cork is floating in the water in the position shown.

Which is the correct position of the cork a time later?

4

T

cork

A. B.

C. D.

(1)

89

76. A source of sound is placed near the open end of a cylindrical tube that lies on a horizontal

table. The tube has some powder sprinkled along its length. The powder collects in piles along

the length of the tube as shown below.

source of sound d

The distance between two consecutive piles of powder is d and the speed of sound in the tube is

v. The frequency of the source is

A.

.2d

v

B. .

d

v

C. dv.

D. 2dv.(1)

90

77. The diagram below shows two long parallel plates that are oppositely charged. A positive test

charge +q is placed along the dotted line XY.

X

+ q

Y

The charge +q is moved from X to Y. Which one of the following best shows the variation with

distance d from X of the magnitude F of the force on +q?

A. F

0

B. F

0X Y d X Y d

C. F

0

D. F

0X Y d X Y d

(1)

91

78. Travelling waves

(a) Graph 1 below shows the variation with time t of the displacement d of a travelling

(progressive) wave. Graph 2 shows the variation with distance x along the same wave of

its displacement d.

t / s

x / cm

4

2

0

–2

–4

4

2

0

–2

–4

0.0 0.1 0.2 0.3 0.4 0.5 0.6

2.42.01.61.20.80.40.0

Graph 1d / mm

Graph 2d / mm

(i) State what is meant by a travelling wave.

.........................................................................................................................

.........................................................................................................................(1)

92

(ii) Use the graphs to determine the amplitude, wavelength, frequency and speed of the

wave.

Amplitude: .................................................................................................(1)

Wavelength: .................................................................................................(1)

Frequency: .................................................................................................

.................................................................................................(1)

Speed: .................................................................................................

.................................................................................................(1)

93

Refraction of waves

(b) The diagram below shows plane wavefronts incident on a boundary between two media

A and B.

medium A

medium B

The ratio

.4.1isA medium ofindex refractive

B medium ofindex refractive

The angle between an incident wavefront and the normal to the boundary is 50°.

(i) Calculate the angle between a refracted wavefront and the normal to the boundary.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(3)

(ii) On the diagram above, construct three wavefronts to show the refraction of the

wave at the boundary.(3)

(Total 11 marks)

94

79. A well-insulated container is divided into two equal volumes by a wall. In one half there is an

ideal gas and the other is a vacuum as shown below.

gas vacuum gas

The wall is now removed. Which one of the following correctly gives the changes, if any, that

take place in the internal energy and entropy of the gas?

Internal energy Entropy

A. stays the same stays the same

B. stays the same increases

C. decreases stays the same

D. decreases increases

(1)

80. The distance S2N – S1N is equal to

A.

.2 f

c

B.

.

f

c

C.

.2c

f

D.

.

c

f

(1)

95

81. A stationary source emits sound of frequency f0. An observer is moving towards the source at

constant speed along the path indicated by the dotted line. The observer passes very close to the

source at time T.

observer

stationary source

Which one of the following graphs best shows the variation with time t of the frequency f heard

by the observer?

A. f

f0

B. f

f0

T t T t

C. f

f0

D. f

f0

T t T t

(1)

96

82. This question is about wave phenomena and the particle nature of light.

Travelling waves

(a) Graph 1 below shows the variation with time t of the displacement d of a travelling

(progressive) wave. Graph 2 shows the variation with distance x along the same wave of

its displacement d.

t / s

x / cm

4

2

0

–2

–4

4

2

0

–2

–4

0.0 0.1 0.2 0.3 0.4 0.5 0.6

2.42.01.61.20.80.40.0

Graph 1d / mm

Graph 2d / mm

(i) State what is meant by a travelling wave.

.........................................................................................................................

.........................................................................................................................(1)

97

(ii) Use the graphs to determine the amplitude, wavelength, frequency and speed of the

wave.

Amplitude: .................................................................................................(1)

Wavelength: .................................................................................................(1)

Frequency: .................................................................................................

.................................................................................................(1)

Speed: .................................................................................................

.................................................................................................(1)

Refraction of waves

(b) The diagram below shows plane wavefronts incident on a boundary between two media

A and B.

medium A

medium B

The ratio

.4.1isA medium ofindex refractive

B medium ofindex refractive

The angle between an incident wavefront and the normal to the boundary is 50°.

98

(i) Calculate the angle between a refracted wavefront and the normal to the boundary.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(3)

(ii) On the diagram above, construct three wavefronts to show the refraction of the

wave at the boundary.(3)

Interference of waves

(c) State two conditions necessary to produce observable interference between light from

two sources.

1. .........................................................................................................................

2. .........................................................................................................................(2)

(d) A Young’s double slit experiment for red light is set up as shown below.

source of

white light

red filter double slit

single slit

screen

(not to scale)

An interference pattern of light and dark fringes is observed on the screen.

99

(i) The red filter is now replaced by a blue filter. State and explain the change in

appearance, other than change of colour, of the fringes on the screen.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(2)

(ii) The filter in (i) is removed. State and explain the appearance of the central

maximum fringe and also of fringes that are away from this central position.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(4)

Particle nature of light

(e) The photo-electric effect cannot be explained on the basis of a wave theory of

electromagnetic radiation. State two experimental observations, other than the existence

of a threshold frequency, that led to this conclusion.

1. .........................................................................................................................

.........................................................................................................................

2. .........................................................................................................................

.........................................................................................................................(2)

100

(f) Monochromatic light is incident on a metal surface in a photo-cell as shown below.

µA

monochromatic

light

The metal surface has work function 2.4 eV and the threshold wavelength for light

incident on the surface is λS. The current in the photo-cell is measured using a

microammeter.

Calculate the threshold wavelength λS.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................(3)

(g) Light of wavelength

and intensity I is incident on the metal surface in (f). (IntensityS2

1 λ

is the light power incident per unit area.) The current in the photo-cell is iP.

State and explain the effect on the current iP in the photo-cell for light incident on the

surface

(i) of wavelength

and intensity 2I;S2

1 λ

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(3)

101

(ii) of wavelength less than

and intensity I.S2

1 λ

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(3)

(Total 30 marks)

83. A wave is travelling through a medium. The diagram shows the variation with time t of the

displacement d of a particle of the medium from t = 0 to t = 25 ms.

1.5

1

0.5

0

–0.5

–1

–1.5

2520151050

d/cm

t/ms

Which of the following correctly gives the frequency and the amplitude of the wave?

frequency / Hz amplitude / cm

A. 2.0 × 10–2 2.0

B. 2.0 × 10–2 1.0

C. 50 2.0

D. 50 1.0

(1)

102

84. Waves of frequency f travel with speed c in air and enter a medium M of refractive index 1.5.

Which of the following correctly gives the frequency and speed of the waves in the medium M?

frequency speed

A. f 5.1

c

B. f 1.5c

C. 1.5f c

D. 5.1

fc

(1)

103

85. Plane wavefronts are incident on a barrier as shown below.

barrier

Which of the following best shows the shape of the wavefronts on the other side of the barrier?

A. B.

C. D.

(1)

104

86. Waves on a string

A travelling wave is created on a string. The graph below shows the variation with time t of the

displacement y of a particular point on the string.

2.0

1.0

0.0

–1.0

–2.0

0.50.40.30.20.10.0

t / ms

Graph 1 / mmy

The variation with distance x of the displacement y of the string at t = 0 is shown below.

2.0

1.0

0.0

–1.0

–2.0

0.50.40.30.20.10.0

x / cm

Graph 2 / mmy

(a) Use information from the graphs to calculate, for this wave,

(i) the wavelength;

.........................................................................................................................(1)

(ii) the frequency;

.........................................................................................................................(2)

(iii) the speed of the wave.

.........................................................................................................................(1)

105

(b) The wave is moving from left to right and has period T.

(i) On graph 1, draw a labelled line to indicate the amplitude of the wave.(1)

(ii) On graph 2, draw the displacement of the string at

.4

Tt=

(2)

(Total 7 marks)

87. A police car, sounding its siren, is travelling at constant speed towards a stationary observer.

The sound emitted by the siren is of constant frequency. The frequency of the sound as heard

by the observer is higher than that heard by the driver of the police car. The reason for this is

that

A. the wavefronts received by the observer are closer together than the wavefronts received

by the driver.

B. the speed of the wavefronts is greater as measured by the observer than by the driver.

C. the speed of the wavefronts is less as measured by the observer than by the driver.

D. the wavefronts received by the observer are further apart than the wavefronts received by

the driver.(1)

88. The light waves emitted by two coherent sources overlap and form an observable interference

pattern. The word coherent in this situation means that

A. the sources are point sources.

B. there is a constant phase difference between the light waves emitted by the sources.

C. the sources emit light of the same frequency.

D. the sources emit light of the same amplitude.(1)

106

89. Waves on a string

A travelling wave is created on a string. The graph below shows the variation with time t of the

displacement y of a particular point on the string.

Graph 1 / mmy 2.0

1.0

0.0

–1.0

–2.0

0.0 0.1 0.2 0.3 0.4 0.5 t / ms

The variation with distance x of the displacement y of the string at t = 0 is shown below.

Graph 2 / mmy 2.0

1.0

0.0

–1.0

–2.0

0.0 1.0 2.0 3.0 4.0 5.0 x / cm

(a) Use information from the graphs to calculate, for this wave,

(i) the wavelength;

.........................................................................................................................(1)

(ii) the frequency;

.........................................................................................................................(2)

(iii) the speed of the wave.

.........................................................................................................................(1)

107

(b) The wave is moving from left to right and has period T.

(i) On graph 1, draw a labelled line to indicate the amplitude of the wave.(1)

(ii) On graph 2, draw the displacement of the string at

.4

Tt=

(2)

(c) One end of the string is attached to a wall. A student creates a single pulse in the string

that travels to the right as shown in the diagram below.

string pulse wall

(i) In the space below, draw a diagram to show the shape and size of the pulse after it

has been reflected from the wall.(2)

(ii) By reference to Newton’s third law, explain the nature of the reflected pulse that

you have drawn in (c)(i) above.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(2)

108

(d) The free end of the string in (c) is now made to oscillate with frequency f such that a

standing wave is established on the string. The diagram below illustrates the standing

wave.

free end

wall

(i) Explain, by reference to the principle of superposition, the formation of a standing

wave.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(3)

(ii) The length of the string is 3.0 m. Using your answer for the speed of the wave in

(a)(iii) calculate the frequency f.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(2)

109

(e) A satellite orbits the Earth at a fixed height above the equator. Two coherent radio

transmitters on the equator emit radio waves of equal amplitude as illustrated in the

diagram below.

satellite orbit

satellite

Earth radio transmitters

not to scale

The signal that the satellite receives varies in intensity.

(i) State what is meant by coherent sources.

.........................................................................................................................

.........................................................................................................................(1)

(ii) Suggest why the signal received by the satellite varies in intensity.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(2)

110

(iii) The transmitters have a separation of 160 m and emit waves of wavelength 1.2 m.

The signal received by the satellite varies in intensity with a frequency of 3.0 Hz

as it flies overhead. The speed of the satellite is 7.7 km s–1.

Calculate the height of the satellite above the Earth’s surface.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(3)

(Total 22 marks)

90. Which of the following best describes the wave speed of a progressive wave travelling through

a medium?

A. The maximum speed of the vibrating particles of the medium

B. The average speed of the vibrating particles of the medium

C. The speed of the medium through which the wave travels

D. The speed of transfer of energy through the medium(1)

111

91. Which of the following diagrams best shows the path of a ray of monochromatic light through a

glass prism in air?

glass

air

glass

air

glass

air

glass

air

A. B.

C.D.

(1)

92. Plane parallel wavefronts are incident on an obstacle. Which of the following diagrams best

shows the diffraction of the waves around the obstacle?

A. B.

C. D.

(1)

112

93. A vibrating tuning fork is held above the top of a tube that is filled with water. The water

gradually runs out of the tube until a maximum loudness of sound is heard.

Which of the following best shows the standing wave pattern set up in the tube at this position?

A. B. C. D.

(1)

94. Which of the following is a correct description of the Doppler effect?

A. Change in frequency of light due to motion of the source of light.

B. Change in frequency of light due to relative motion between the source of light and the

observer.

C. Change in observed frequency of light due to relative motion between the source of light

and the observer.

D. Change in observed frequency of light due to change in velocity of the source of light.(1)

113

95. In a double-slit experiment using coherent light of wavelength λ, the central bright fringe is

observed on a screen at point O, as shown below.

coherent light

wavelength λ

screen

P

O

(not to scale)

double slit

At point P, the path difference between light arriving at P from the two slits is 4λ.

Which of the following correctly describes the observed fringe pattern?

nature of fringe at P number of dark fringes between O and P

A. bright 3

B. bright 4

C. dark 3

D. dark 4

(1)

96. This question is about some properties of waves associated with the principle of superposition.

Stationary (standing) waves and resonance

(a) State two ways in which a standing wave differs from a continuous wave.

1. .........................................................................................................................

.........................................................................................................................

2. .........................................................................................................................

.........................................................................................................................(2)

114

115

(b) State the principle of superposition as applied to waves.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................(2)

(c) A stretched string is fixed at one end. The other end is vibrated continuously to produce a

wave along the string. The wave is reflected at the fixed end and as a result a standing

wave is set up in the string.

The diagram below shows the displacement of the string at time t = 0. The dotted line

shows the equilibrium position of the string.

free end

fixed end

116

(i) The period of oscillation of the string is T. On the diagrams below, draw sketches

of the displacement of the string at time

and at time 4

Tt = .

2

Tt=

4

Tt =

2

Tt =

(2)

(ii) Use your sketches in (i) to explain why the wave in the string appears to be

stationary.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(2)

117

(d) Stationary waves are often associated with the phenomenon of resonance.

(i) Describe what is meant by resonance.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(2)

(ii) On 19 September 1985 an earthquake occurred in Mexico City. Many buildings

that were about 80 m tall collapsed whereas buildings that were taller or shorter

than this remained undamaged. Use the data below to suggest a reason for this.

period oscillation of an 80 m tall building = 2.0 s

speed of earthquake waves = 6.0 × 103 m s–1

average wavelength of the waves = 1.2 × 104 m

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(3)

(Total 13 marks)

97. The phenomenon of diffraction is associated with

A. sound waves only.

B. light waves only.

C. water waves only.

D. all waves.(1)

118

98. The diagram below shows plane wavefronts of a wave that is approaching the boundary

between two media, X and Y. The speed of the wave is greater in medium X than in medium Y.

The wave crosses the boundary.

medium X

boundary

medium Y

Which of the following diagrams is correct?

medium X medium Y medium X medium Y

medium X medium Y medium X medium Y

A. B.

C. D.

(1)

119

99. The graph below shows the variation with time t of the separate displacements d of a medium,

at a particular point in the medium due to two waves, P and Q.

1.0

0.5

0.0

–0.5

–1.0

0

wave Q

wave P

t

d / mm

The amplitude of the wave resulting from the interference of P and Q is

A. 0.0 mm.

B. 1.0 mm.

C. 1.4 mm.

D. 2.0 mm.(1)

100. One end of a long string is vibrated at a constant frequency f. A travelling wave of wavelength

λ and speed v is set up on the string.

The frequency of vibration is doubled but the tension in the string is unchanged. Which of the

following shows the wavelength and speed of the new travelling wave?

Wavelength Speed

A. 2

λv

B. 2

λ2v

C. 2λ v

D. 2λ 2v

(1)

120

101. Wave properties

(a) By reference to the energy of a travelling wave, state what is meant by

(i) a ray.

.........................................................................................................................

.........................................................................................................................(1)

(ii) wave speed.

.........................................................................................................................

.........................................................................................................................(1)

(b) The graph below shows the variation with time t of the displacement xA of wave A as it

passes through a point P.

3.0

2.0

1.0

0.0

–1.0

–2.0

–3.0

10.08.06.04.02.00.0 t / ms

x / mmA

Wave A

121

The graph below shows the variation with time t of the displacement xB of wave B as it

passes through point P.

2.0

1.0

0.0

–1.0

–2.0

10.08.06.04.02.00.0 t / msx / mmB

Wave B

(i) Calculate the frequency of the waves.

.........................................................................................................................

.........................................................................................................................(1)

(ii) The waves pass simultaneously through point P. Use the graphs to determine the

resultant displacement at point P of the two waves at time t = 1.0 ms and at time t

= 8.0 ms.

At t = 1.0 ms: ...............................................................................................

...............................................................................................

At t = 8.0 ms: ...............................................................................................

...............................................................................................(3)

(Total 6 marks)

122

102. A string with both ends fixed is made to vibrate in the second harmonic mode as shown by the

dashed lines in the diagram below.

P

Q

The solid line shows a photograph of the string at a particular instant of time. Two points on the

string have been marked P and Q.

Which of the following correctly compares both the period of vibration of P and Q and the

average speed of P and Q?

Period Average speed

A. same same

B. same different

C. different same

D. different different

(1)

123

103. The diagram below represents the fundamental (first harmonic) standing wave of sound inside a

pipe.

pipe

P Q

Which of the following correctly represents the displacement of the air at P and Q?

A.

B.

C.

D.

P Q

(1)

124

104. X-ray spectra

The graph shows the variation with wavelength λ of the relative intensity of an X-ray spectrum

produced when electrons strike a metal target.

relative intensity

120100806040200

/ nm

The spectrum consists of a continuous spectrum and a line spectrum (the “spikes”).

(a) (i) State why there is a sharp cut-off at the short-wavelength end of the spectrum.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(1)

(ii) Explain why the wavelengths of the line spectrum are characteristic of the target

element.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(3)

125

(b) In 1913, Moseley discovered that the frequency f of a line in the spectrum is related to

the proton number (atomic number) Z of the target atoms by the expression

f = a(Z − b)2,

where a and b are constants.

One line in the spectrum produced by a certain metal target has a wavelength of 0.154

nm. For this line, a = 2.50 × 1015 Hz and b = 1.00.

Calculate the proton number of the target metal.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................(3)

(c) Determine the minimum potential difference through which electrons in the X-ray tube

must be accelerated so that the line of wavelength 0.154 nm may be observed in the

spectrum.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................(3)

(Total 10 marks)

126

105. This question is about diffraction.

Plane wavefronts of monochromatic light of wavelength λ are incident on a rectangular slit of

width b. After passing through the slit, the light is brought to a focus on a screen distance D

from the slit as shown below. The width of the slit is comparable to the wavelength of the

incident light and b << D. The point P on the screen is opposite the centre of the slit.

P

screen

slit

D

b

The sketch graph below shows that the variation with angle θ of the intensity of the light on the

screen.

intensity

= 0

127

(a) Explain qualitatively, this intensity distribution.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................(3)

(b) The angle θ = φ is the angular half-width of the central maximum of the intensity

distribution and is given by the expression φ = Derive an expression in terms of D, λ.

b

λ

and b for the half-width d of the central maximum.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................(2)

128

(c) The single slit is replaced by two rectangular slits of width b. The distance between the

centre of the slits is equal to 2b.

On the axes below, draw a sketch of the intensity distribution on the screen. (The

intensity distribution of a single slit is shown by the dotted line.)

intensity

= 0

(2)

(Total 7 marks)

129

106. A wedge shaped film of air is made by separating two thin, flat glass plates by a spacer.

eye

Pmonochromaticlight source

flat glass plates

spacer

A

It is arranged for light from a monochromatic source to be incident on the plates by reflection

from another glass plate P. The light reflected from the wedge is viewed from above as shown

in the diagram. A system of equally spaced, parallel fringes is observed. (The diagram is not to

scale.)

(a) State what happens to the phase of the light waves reflected from the upper surface of the

plate labelled A in the diagram.

...................................................................................................................................(1)

(b) The wavelength of the light is 560 nm. Calculate by how much the width of the wedge

changes between one bright fringe and the next bright fringe.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................(2)

(Total 3 marks)

130

107. A transverse travelling wave has amplitude A0 and wavelength λ.

The distance between a crest and its neighbouring trough, measured in the direction of energy

transfer of the wave is equal to

A. A0.

B. 2A0.

C. .

2

λ

D. λ.(1)

108. A light wave travelling through a vacuum is incident on a block of glass. What change, if any,

occurs in the frequency and amplitude of the wave as it travels into the glass?

frequency amplitude

A. decreases decreases

B. decreases constant

C. constant decreases

D. constant constant

(1)

109. This question is about waves.

(a) With reference to the direction of energy transfer through a medium, distinguish between

a transverse wave and a longitudinal wave.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................(3)

131

(b) A wave is travelling along the surface of some shallow water in the x-direction. The

graph shows the variation with time t of the displacement d of a particle of water.

–10

10

8

6

4

2

0

–2

–4

–6

–8

0 0.05 0.250.20.150.1 0.3

t / s

d / mm

Use the graph to determine for the wave

(i) the frequency,

...........................................................................................................................

...........................................................................................................................(2)

(ii) the amplitude.

...........................................................................................................................(1)

132

(c) The speed of the wave in (b) is 15 cm s–1. Deduce that the wavelength of this wave is

2.0 cm.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(2)

(d) The graph in (b) shows the displacement of a particle at the position x = 0.

On the axes below, draw a graph to show the variation with distance x along the water

surface of the displacement d of the water surface at time t = 0.070 s.

–10

10

8

6

4

2

0

–2

–4

–6

–8

0 1 432

d / mm

x/cm

(3)

133

(e) The wave encounters a shelf that divides the water into two separate depths. The water to

the right of the shelf is deeper than that to the left of the shelf.

shelf

deep watershallow water

direction of

travel of wave

wave fronts

30°

The angle between the wavefronts in the shallow water and the shelf is 30°. The speed of

the wave in the shallow water is 15 cm s–1 and in the deeper water is 20 cm s–1. For the

wave in the deeper water, determine the angle between the normal to the wavefronts and

the shelf.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(3)

(Total 14 marks)

134

110. Which statement is true for standing (stationary) waves?

A. All points in the wave vibrate in phase.

B. There is no energy in a standing wave.

C. The wavelength of the wave is the distance between adjacent nodes.

D. Neighbouring points in the wave have different amplitudes of vibration.(1)

111. A stationary source of sound emits waves of wavelength λ, period T and speed V. The source

now moves with speed v in a straight line away from a stationary observer.

What are the wavelength and the speed of the wave as detected by the observer?

wavelength speed

A. λ V + v

B. λ – vT V

C. λ V – v

D. λ + vT V

(1)

112. Which two conditions are necessary for observable interference between two light beams?

A. meet at a point constant phase difference

B. constant phase difference similar amplitude

C. same frequency similar amplitude

D. similar amplitude meet at a point(1)

135

113. This question is about waves.

(a) With reference to the direction of energy transfer through a medium, distinguish between

a transverse wave and a longitudinal wave.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(3)

(b) A wave is travelling along the surface of some shallow water in the x-direction. The

graph shows the variation with time t of the displacement d of a particle of water.

–10

10

8

6

4

2

0

–2

–4

–6

–8

0 0.05 0.250.20.150.1 0.3

t / s

d / mm

136

Use the graph to determine for the wave

(i) the frequency,

...........................................................................................................................

...........................................................................................................................(2)

(ii) the amplitude.

...........................................................................................................................(1)

(c) The speed of the wave in (b) is 15 cm s–1. Deduce that the wavelength of this wave is

2.0 cm.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(2)

137

(d) The graph in (b) shows the displacement of a particle at the position x = 0.

On the axes below, draw a graph to show the variation with distance x along the water

surface of the displacement d of the water surface at time t = 0.070 s.

–10

10

8

6

4

2

0

–2

–4

–6

–8

0 1 432

d / mm

x/cm

(3)

(e) The wave encounters a shelf that divides the water into two separate depths. The water to

the right of the shelf is deeper than that to the left of the shelf.

shelf

deep watershallow water

direction of

travel of wave

wave fronts

30 °

138

The angle between the wavefronts in the shallow water and the shelf is 30°. The speed of

the wave in the shallow water is 15 cm s–1 and in the deeper water is 20 cm s–1. For the

wave in the deeper water, determine the angle between the normal to the wavefronts and

the shelf.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(3)

(Total 14 marks)

114. Light travelling from water to air is incident on a boundary.

Y

Z air

X water

W

Which of the following is a correct statement of Snell’s law for this situation?

A. sin Z = constant × sin Y

B. sin W = constant × sin Z

C. sin X = constant × sin Z

D. sin W = constant × sin Y(1)

139

115. A standing wave is established on a string between two fixed points.

TB

AU

C

D

At the instant shown, point T is moving downwards. Which arrow gives the direction of

movement of point U at this instant?

A. A

B. B

C. C

D. D(1)

140

116. A pulse is travelling along a string attached to a wall.

pulse direction

Which of the following shows the shape of the string after reflection from the wall?

A.

B.

C.

D.

(1)

141

117. The diagram below shows the displacement-position graph at a particular instant for a

longitudinal wave travelling along a spring.

displacement to right

displacement to left

+

0

–

C

0 B D

A

position

A positive displacement on the graph indicates that the coils of the spring are displaced to the

right of their equilibrium position.

At which position along the spring is the displacement of two adjacent coils a maximum?

A. A

B. B

C. C

D. D(1)

142

118. The diagrams below show two standing wave patterns that are set up in a stretched string fixed

at both ends. The frequency of pattern 1 is f1 and that of pattern 2 is f2.

pattern 1

pattern 2

frequency f1

frequency f2

The ratio

is2

1

f

f

A. .

3

1

B. .

3

2

C. 3.

D. 6.(1)

119. Sound of a constant frequency f0 is being emitted by a sound source. An observer O travels in

the direction shown at a speed of 0.1 v where v is the speed of sound.

observer

O

sound source

Which of the following gives the relationship between f0 and the frequency f of observed

sound?

A. f = 1.1f0

B. f0 < f < 1.1f0

C. f = 0.9f0

D. f0 > f > 0.9f0(1)

143

120. This question is about wave phenomena.

(a) The graph below shows the variation with time t of the displacement x of one particle in

a sound wave.

x/mm 0.3

0.2

0.1

0.0

–0.1

–0.2

–0.3

t/ms

0.0 0.1 0.2 0.3 0.4 0.5 0.6

The speed of the wave is 380 m s–1.

(i) Suggest, by marking the letter C on the t-axis of the graph above, one time at

which the particle could be at the centre of a compression.(1)

(ii) Deduce the wavelength of the wave.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(3)

(b) (i) Outline the conditions necessary for the formation of a standing (stationary) wave.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(2)

144

(ii) A horizontal tube, closed at one end, has some fine powder sprinkled along its

length. A source S of sound is placed at the open end of the tube, as shown below.

source S

heap of powder

The frequency of the source S is varied. Explain why, at a particular frequency, the

powder is seen to form small equally-spaced heaps in the tube.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(2)

(iii) The mean separation of the heaps of powder in (b)(ii) is 9.3 cm when the

frequency of the source S is 1800 Hz. Calculate the speed of sound in the tube.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(2)

(c) The experiment in (b)(ii) is repeated on a day when the temperature of the air in the tube

is higher. The mean separation of the heaps is observed to have increased for the same

frequency of the source S. Deduce qualitatively the effect, if any, of temperature rise on

the speed of the sound in the tube.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(2)

145

(d) The diagram below shows wavefronts produced by two sources S1 and S2 of sound that

are vibrating in phase.

B A B

S1

S2

The waves interfere constructively along the lines labelled A and B.

(i) State what is meant by constructive interference.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(3)

(ii) On the diagram above, draw another line, labelled C, along which the waves

interfere constructively.(1)

(iii) On the diagram above, draw another line, labelled D, along which the waves

interfere destructively.(1)

(Total 17 marks)

146

121. The graph below shows the variation with time t of the displacement x of a particle undergoing

simple harmonic motion.

Which graph correctly shows the variation with time t of the acceleration a of the particle?

(1)

147

122. A wooden block is at rest on a horizontal frictionless surface. A horizontal spring is attached

between the block and a rigid support.

The block is displaced to the right by an amount X and is then released. The period of

oscillations is T and the total energy of the system is E.

For an initial displacement of which of the following shows the best estimate for the period

2

X

of oscillations and the total energy of the system?

Period Total energy

A. T 2

E

B. T 4

E

C. 2

T

2

E

D. 2

T

4

E

(1)

123. Which of the following correctly describes the change, if any, in the speed, wavelength and

frequency of a light wave as it passes from air into glass?

Speed Wavelength Frequency

A. decreases decreases unchanged

B. decreases unchanged decreases

C. unchanged increases decreases

D. increases increases unchanged

(1)

148

149

124. The diagram below shows a pulse travelling along a rope from X to Y. The end Y of the rope is

tied to a fixed support.

When the pulse reaches end Y it will

A. disappear.

B. cause the end of the rope at Y to oscillate up and down.

C. be reflected and be inverted.

D. be reflected and not be inverted.(1)

125. Simple harmonic motion and the greenhouse effect

(a) A body is displaced from equilibrium. State the two conditions necessary for the body to

execute simple harmonic motion.

1. .........................................................................................................................

.........................................................................................................................

2. .........................................................................................................................

.........................................................................................................................(2)

150

(b) In a simple model of a methane molecule, a hydrogen atom and the carbon atom can be

regarded as two masses attached by a spring. A hydrogen atom is much less massive than

the carbon atom such that any displacement of the carbon atom may be ignored.

The graph below shows the variation with time t of the displacement x from its

equilibrium position of a hydrogen atom in a molecule of methane.

The mass of hydrogen atom is 1.7 × 10–27 kg. Use data from the graph above

(i) to determine its amplitude of oscillation.

.........................................................................................................................(1)

(ii) to show that the frequency of its oscillation is 9.1 × 1013 Hz.

.........................................................................................................................

.........................................................................................................................(2)

(iii) to show that the maximum kinetic energy of the hydrogen atom is 6.2 × 10–18 J.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(2)

151

(c) On the grid below, sketch a graph to show the variation with time t of the speed v of the

hydrogen atom for one period of oscillation starting at t = 0. (There is no need to add

values to the speed axis.)

(3)

(d) Assuming that the motion of the hydrogen atom is simple harmonic, its frequency of

oscillation f is given by the expression

,2

1

pm

kf

π

=

where k is the force per unit displacement between a hydrogen atom and the carbon atom

and mp is the mass of a proton.

(i) Show that the value of k is approximately 560 N m–1.

.........................................................................................................................

.........................................................................................................................(1)

(ii) Estimate, using your answer to (d)(i), the maximum acceleration of the hydrogen

atom.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(2)

152

(e) Methane is classified as a greenhouse gas.

(i) Describe what is meant by a greenhouse gas.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(2)

(ii) Electromagnetic radiation of frequency 9.1 × 1013 Hz is in the infrared region of

the electromagnetic spectrum. Suggest, based on the information given in (b)(ii),

why methane is classified as a greenhouse gas.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(2)

(Total 17 marks)

153

126. The graph below shows the variation with time t of the displacement x of a particle undergoing

simple harmonic motion.

Which graph correctly shows the variation with time t of the acceleration a of the particle?

(1)

154

127. The two graphs show the variation with time of the individual displacements of two waves as

they pass through the same point.

The displacement of the resultant wave at the point at time T is equal to

A. x1 + x2.

B. x1 – x2 .

C. A1 + A2.

D. A1 – A2.

(1)

155

128. A tube is filled with water and a vibrating tuning fork is held above its open end.

The tap at the base of the tube is opened. As the water runs out, the sound is loudest when the

water level is a distance x below the top of the tube. A second loud sound is heard when the

water level is a distance y below the top. Which of the following is a correct expression for the

wavelength λ of the sound produced by the tuning fork?

A. λ = y

B. λ = 2x

C. λ = y − x

D. λ = 2(y − x)(1)

156

129. A source S, moving at constant speed, emits a sound of constant frequency. The source passes

by a stationary observer O, as shown below.

Which of the following shows the variation with time t of the frequency f observed at O as the

source S approaches and passes by the observer?

(1)

130. Simple harmonic motion and the greenhouse effect

(a) A body is displaced from equilibrium. State the two conditions necessary for the body to

execute simple harmonic motion.

1. .........................................................................................................................

.........................................................................................................................

2. .........................................................................................................................

.........................................................................................................................(2)

157

(b) In a simple model of a methane molecule, a hydrogen atom and the carbon atom can be

regarded as two masses attached by a spring. A hydrogen atom is much less massive than

the carbon atom such that any displacement of the carbon atom may be ignored.

The graph below shows the variation with time t of the displacement x from its

equilibrium position of a hydrogen atom in a molecule of methane.

The mass of hydrogen atom is 1.7 × 10–27 kg. Use data from the graph above

(i) to determine its amplitude of oscillation.

.........................................................................................................................(1)

(ii) to show that the frequency of its oscillation is 9.1 × 1013 Hz.

.........................................................................................................................

.........................................................................................................................(2)

(iii) to show that the maximum kinetic energy of the hydrogen atom is 6.2 × 10–18 J.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(2)

158

(c) Assuming that the motion of the hydrogen atom is simple harmonic, its frequency of

oscillation f is given by the expression

,2

1

pm

kf

π

=

where k is the force per unit displacement between a hydrogen atom and the carbon atom

and mp is the mass of a proton.

(i) Show that the value of k is approximately 560 N m–1.

.........................................................................................................................

.........................................................................................................................(1)

(ii) Estimate, using your answer to (c)(i), the maximum acceleration of the hydrogen

atom.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(2)

159

(d) Methane is classified as a greenhouse gas.

(i) Describe what is meant by a greenhouse gas.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(2)

(ii) Electromagnetic radiation of frequency 9.1 × 1013 Hz is in the infrared region of

the electromagnetic spectrum. Suggest, based on the information given in (b)(ii),

why methane is classified as a greenhouse gas.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................(2)

(Total 14 marks)

160