physics waves mcq

10 - WAVES Page 1 ( Answers at the end of all questions )

1 ) When two tuning forks ( fork 1 and fork 2 ) are sounded simultaneously, 4 beats per second are heard. Now, some tape is attached on the prong of fork 2. When the tuning forks are sounded again, 6 beats per second are heard. If the frequency of fork 1 is 200 Hz, then what was the original frequency of fork 2 ?

( a ) 202 Hz ( b ) 200 Hz ( c ) 204 Hz ( d ) 196 Hz [ AIEEE 2005 ]

2 ) An observer moves towards a stationary source of sound with a velocity one-f fth of the velocity of sound. What is the percentage increase in the apparent freq ency ?

( a ) 0.5 % ( b ) zero ( c ) 20 ( d ) 5 % [ AIEEE 2005 ] 3 ) The displacement y of a particle in a medium can be expresse as y 10 6 sin ( 100t + 20x + 4 ) m, where t is in second and x in metre. The speed of

the wave is ( a ) 2000 m/s ( b ) 5 m s ( c ) 20 m/s ( d ) 5 m/s [ AIEEE 2004 ] 4 ) The displacement y of a wave travelling in the x direction is given by y 10 4 sin ( 600t - 20x + 3 ) metres, here x is expressed in metres and t in

seconds. The speed of the wave motion is ( a ) 200 m/s ( b ) 300 m/s ( c ) 600 m s ( d ) 1200 m/s [ AIEEE 2003 ] 5 ) A tuning fork of frequency 256 Hz makes 5 beats per second with the vibrating string of

a piano. The beat frequency decr ses to 2 beats per second, when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was

( a ) ( 256 + 2 ) Hz ( b ) ( 256 + 5 ) Hz ( c ) ( 256 - 2 ) Hz ( d ) ( 256 - 5 ) Hz [ AIEEE 2003 ]

6 ) The displacement of a wave i given by the equation y = 2 sin ( / 1.6 ) ( 64t - x ). The frequency of the wave is


7 ) Transverse are g nerated in two uniform wires A and B by attaching their free ends to a vibrating source of frequency 600 Hz. The diameter of wire A is one-third that of wire B and tension in the wire A is double that in wire B. What is the ratio of velocities of waves of waves in wire A and B ?

( a ) 3 2 ( b ) 2 : 3 ( c ) 3 : 2 ( d ) 2 : 3 [ AIEEE 2002 ] 8 ) If the phase difference between two points is 60 on a wave velocity of 360 m /s and

frequency 500 Hz, then path difference between the two points is ( a ) 1 cm ( b ) 6 cm ( c ) 12 cm ( d ) 24 cm [ AIEEE 2002 ]

9 ) A resonance air column of length 40 cm resonates with a tuning fork of frequency 450 Hz. Ignoring end correction, the velocity of sound in air will be

( a ) 720 m /s ( b ) 820 m /s ( c ) 920 m /s ( d ) 1020 m /s [ AIEEE 2002 ] 10 ) An observer is moving towards a stationary source of frequency 250 Hz with a velocity

of 40 m /s. If the velocity of sound is 330 m /s, the apparent frequency heard by the observer will be


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forks are sounded again, 6 beats per second are heard. If the frequency of fork 1 is 200

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forks are sounded again, 6 beats per second are heard. If the frequency of fork 1 is 200

( a ) 202 Hz ( b ) 200 Hz ( c ) 204 Hz ( d ) 196 Hz [ AIEE

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E 2005 ]

2 ) An observer moves towards a stationary source of sound with a velocity one-f fth of the

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.com2 ) An observer moves towards a stationary source of sound with a velocity one-f fth of the velocity of sound. What is the percentage increase in the apparent freq ency ?

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.comvelocity of sound. What is the percentage increase in the apparent freq ency ? [ AIEEE 2005 ]

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.com [ AIEEE 2005 ]

3 ) The displacement y of a particle in a medium can be expresse as

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3 ) The displacement y of a particle in a medium can be expresse as 4 ) m, where t is in second and x in metre. The speed of

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4 ) m, where t is in second and x in metre. The speed of

s [ AIEEE 2004 ]

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s [ AIEEE 2004 ]

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4 ) The displacement y of a wave travelling in the x

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4 ) The displacement y of a wave travelling in the x

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direction is given by

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direction is given by 3 ) metres, here x is expressed in metres and t in

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3 ) metres, here x is expressed in metres and t in seconds. The speed of the wave motion is

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seconds. The speed of the wave motion is s ( c ) 600 m

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s ( c ) 600 m

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s ( d ) 1200 m

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s ( d ) 1200 m

5 ) A tuning fork of frequency 256 Hz makes 5

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5 ) A tuning fork of frequency 256 Hz makes 5 beats per second with the vibrating string of

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beats per second with the vibrating string of a piano. The beat frequency decr ses to 2 beats per second, when the tension in the

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a piano. The beat frequency decr ses to 2 beats per second, when the tension in the piano string is slightly increased. The frequency of the piano string before increasing

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piano string is slightly increased. The frequency of the piano string before increasing

( a ) ( 256 + 2 ) Hz ( b ) ( 256 + 5 ) Hz ( c ) ( 256

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( a ) ( 256 + 2 ) Hz ( b ) ( 256 + 5 ) Hz ( c ) ( 256

6 ) The displacement of a wave i given by the equation y

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6 ) The displacement of a wave i given by the equation y frequency of the wave is

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frequency of the wave is

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( a ) 30 Hz ( b ) 25 Hz ( c ) 20 Hz ( d ) 15 Hz [

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( a ) 30 Hz ( b ) 25 Hz ( c ) 20 Hz ( d ) 15 Hz [

7 ) Transverse are g nerated in two uniform wires A and B b attachin their free ends to

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7 ) Transverse are g nerated in two uniform wires A and B by attaching their free ends to a vibrating source of frequency 600 Hz. The diameter of wire A is one-third that of wire

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a vibrating source of frequency 600 Hz. The diameter of wire A is one-third that of wire B and tension in the wire A is double that in wire B. What is the ratio of veloc ties of

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B and tension in the wire A is double that in wire B. What is the ratio of veloc ties of waves of waves in wire A and B ?

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waves of waves in wire A and B ? ( a )

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( a )

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3 2 ( b ) 2 :

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3 2 ( b ) 2 :

8 ) If the phase difference between two points is 60

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8 ) If the phase difference between two points is 60 frequency 500 Hz, then path differ

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frequency 500 Hz, then path differ ( a ) 1 cm ( b ) 6 cm ( c ) 12 cm ( d ) 24 cm [ A

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( a ) 1 cm ( b ) 6 cm ( c ) 12 cm ( d ) 24 cm [ A

9 ) A resonance air column of length 40 cm resonates with a tuning fork of frequency 450 www.

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9 ) A resonance air column of length 40 cm resonates with a tuning fork of frequency 450

( a ) 720 m www.

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( a ) 720 m


11 ) An open pipe is in resonance in second harmonic with frequency f1. Now one end of the tube is closed and frequency is increased to f2 such that the resonance again occurs in nth harmonic. Choose the correct option.

( a ) n = 3, f2 = ( 3 / 4 ) f1 ( b ) n = 3, f2 = ( 5 / 4 ) f1 ( c ) n = 5, f2 = ( 5 / 4 ) f1 ( d ) n = 5, f2 = ( 3 / 4 ) f1 [ I T 2005 ]

12 ) A tuning fork of 512 Hz is used to produce resonance in a resonance ube experiment. The level of water at first resonance is 30.7 cm and at second reso ance is 63.2 cm. The maximum possible error in calculating velocity of sound in cm s is

( a ) 204.8 ( b ) 102.4 ( c ) 51.2 ( d ) 153.60 [ IIT 2005 ]

13 ) A closed organ pipe of length L and an open organ pipe contain gases of densities 1 and 2 respectively. The compressibility of gases are equal in both the pipes.

Both the pipes are vibrating in their first overtone wi h the same frequency. The length of the organ pipe is

( a ) 3L ( b )

34L ( c )

2

1

34L ( d )

34L

1

2 [ IIT 2004 ]

14 ) A source of sound of frequency 600 Hz is placed inside water. The speed of sound in water is 1500 m/s and in air it is 300 m/s . The frequency of sound recorded by an observer who is standing in air is

( a ) 200 Hz ( b ) 3000 Hz c ) 20 Hz ( d ) 600 Hz [ IIT 2004 ]

15 ) A police car moving a 22 m s, chases a motorcyclist. The police man sounds his horn at 76 H , while both of them move t wards a stationary siren f requency 165 Hz. Calculate the speed of the motorcycle, if it is given that he does not observe any beats.

( a ) 33 m / s ( b ) 22 m / s ( c ) zero ( d ) 11 m / s [ IIT 2003 ] 16 ) In th experiment for the determination of the speed of sound in air using the

resonance column method, the length of the air column that resonates in the fundamental mode, with a tuning fork is 0.1 m. When this length is changed to 0.35 m, the same tuning fork resonates with the first overtone. Calculate the end correction.

( a ) 0.012 m ( b ) 0.025 m ( c ) 0.05 m ( d ) 0.024 m [ IIT 2003 ]

17 ) A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger sitting in a moving train A records a frequency of 5.5 kHz while the train approaches the siren. During his return journey in a different train B he records a frequency of 6.0 kHz while approaching the same siren. The ratio of velocity of train B to that of train A is

( a ) 242 / 252 ( b ) 2 ( c ) 5 6 ( d ) 11 / 6 [ IIT 2002 ] 18 ) A sonometer wire resonates with a given tuning fork forming standing waves with five

antinodes between the two bridges when a mass of 9 kg is suspended from the wire. When this mass is replaced by mass M, the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of M is

( a ) 25 kg ( b ) 5 kg ( c ) 12.5 kg ( d ) 1 25 kg [ IIT 2002 ]

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[ I T 2005 ]

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[ I T 2005 ]

12 ) A tuning fork of 512 Hz is used to produce resonance in a resonance ube experiment.

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.com12 ) A tuning fork of 512 Hz is used to produce resonance in a resonance ube experiment. The level of water at first resonance is 30.7 cm and at second reso ance is 63.2 cm.

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.comThe level of water at first resonance is 30.7 cm and at second reso ance is 63.2 cm. The maximum possible error in calculating velocity of sound in cm

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.comThe maximum possible error in calculating velocity of sound in cm

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( a ) 204.8 b ) 102.4 ( c ) 51.2 ( d ) 153.60

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( a ) 204.8 b ) 102.4 ( c ) 51.2 ( d ) 153.60 [ IIT 2005 ]

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[ IIT 2005 ]

13 ) A closed organ pipe of length L and an open organ pipe contain gases of densities

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13 ) A closed organ pipe of length L and an open organ pipe contain gases of densities respectively. The compressibility of gases are equal in both the pipes.

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respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone wi h the same frequency. The length

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Both the pipes are vibrating in their first overtone wi h the same frequency. The length

( d )

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( d )

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3

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34L

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4L

14 ) A source of sound of frequency 600 Hz is placed inside water. The speed of sound in

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14 ) A source of sound of frequency 600 Hz is placed inside water. The speed of sound in s and in air it is 300 m

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s and in air it is 300 m/

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/

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s . The frequency of sound recorded by an

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s . The frequency of sound recorded by an observer who is standing in air is

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observer who is standing in air is ( a ) 200 Hz ( b ) 3000 Hz c ) 20 Hz ( d ) 600 Hz [

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( a ) 200 Hz ( b ) 3000 Hz c ) 20 Hz ( d ) 600 Hz [

15 ) A police car moving a 22 m

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15 ) A police car moving a 22 m

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chases a motorcyclist. The police man

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chases a motorcyclist. The police man sounds his horn at 76 H , while

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sounds his horn at 76 H , while both of them move t wards a

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both of them move t wards a stationary siren f requency 165 Hz.

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stationary siren f requency 165 Hz. Calculate the speed of the motorcycle,

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Calculate the speed of the motorcycle, if it is given that he does not

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if it is given that he does not observe any beats.

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observe any beats. ( a ) 33 m

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( a ) 33 m /

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/

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s ( b ) 22 m

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s ( b ) 22 m s ( b ) 22 m

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s ( b ) 22 m

16 ) In th experiment for the determination of the speed of sound in air using the

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16 ) In th experiment for the determination of the speed of sound in air using the resonance column method, the length of the air column that resonates in the

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resonance column method, the length of the air column that resonates in the fundamental mode, with a tuning fork is 0.1 m. When this length is changed to 0.35 m,

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fundamental mode, with a tuning fork is 0.1 m. When this length is changed to 0.35 m,

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the same tuning fork resonates with the first overtone. Calculate the end correction.

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the same tuning fork resonates with the first overtone. Calculate the end correction. ( a ) 0.012 m ( b ) 0.025 m ( c ) 0.05 m ( d ) 0.024 m [

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( a ) 0.012 m ( b ) 0.025 m ( c ) 0.05 m ( d ) 0.024 m [

17 ) A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger www.

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17 ) A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger


19 ) The ends of a stretched wire of length L are fixed at x = 0 and x = L. In one

experiment, the displacement of the wire is y1 = A sin Lx

sin t and energy is E1

and in another experiment, its displacement is y2 = A sin L

x2 sin 2 t nd energy is

E2. Then ( a ) E2 = E1 ( b ) E2 = 2E1 ( c ) E2 = 4E1 ( d ) E2 = 16E1 [ IIT 2001 ]

20 ) Two pulses in a stretched string, whose centres are initially 8 cm apart, are moving towards each other as shown in the figure. The speed of each pulse is 2 cm/s. After 2 seconds, the total energy of the pulses will be

( a ) zero ( b ) purely kinetic ( c ) purely potential ( d ) partly kinetic and partly potential

[ IIT 2001 ]

21 ) A train moves towards a stationary observe w th speed 34 m / s. The train sounds a whistle and its frequency registered by t e observer is f1. If the speed of the train is reduced to 17 m s, the frequency registered is f2. If the speed of sound is 340 m s, then the ratio f1 f2 is

( a ) 18 19 ( b ) 1 / 2 ( ) 2 ( d ) 19 / 18 [ IIT 2000 ]

22) Two vibrating strings o the same material but lengths L and 2L have radii 2r and r respectively. They are st etched under the same tension. Both the strings vibrate in their fundamental mode , the one of length L with frequency 1 and the other with frequency

2. The ratio 1 2 is given by ( a ) 2 ( b ) ( c ) 8 ( d ) 1 [ IIT 2000 ]

23 ) Two monoatomic ideal gases 1 and 2 of molecular masses m1 and m2 respectively are enclosed in separate containers kept at the same temperature. Te ratio of the speed of sound in gas 1 to that in gas 2 is given by

( a ) 21

mm

( b ) 12

mm

( c ) 21

mm

( d ) 12

mm

[ IIT 2000 ]

24 ) The ratio of the speed of sound in nitrogen gas to that in helium gas at 300 K is

( a ) 72 ( b )

71 ( c )

53 ( d )

56 [ IIT 1999 ]

25 ) As a wave propagates ( a ) the wave intensity remains constant for a plane wave ( b ) the wave intensity decreases as the inverse of the distance from the source for a

spherical wave ( c ) the wave intensity decreases as the inverse of the square of the distance from the

source for a spherical wave. ( d ) total intensity of the spherical wave over the spherical surface centered at the

source remains constant at all times. [ IIT 1999 ]

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.comt nd energy is = 16E

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.com = 16E1

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.com1 [ IIT 2001 ]

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20 ) Two pulses in a stretched string, whose centres are initially

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20 ) Two pulses in a stretched string, whose centres are initially 8 cm apart, are moving towards each other as shown in the

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8 cm apart, are moving towards each other as shown in the s. After 2 seconds,

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s. After 2 seconds,

( a ) zero ( b ) purely kinetic ( c ) purely potential

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( a ) zero ( b ) purely kinetic ( c ) purely potential ( d ) partly kinetic and partly potential

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( d ) partly kinetic and partly potential

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21 ) A train moves towards a stationary observe w th speed 34 m

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21 ) A train moves towards a stationary observe w th speed 34 m whistle and its frequency registered by t e observer is f

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whistle and its frequency registered by t e observer is f s, the frequency registered is f

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s, the frequency registered is f

2 ( ) 2 ( d ) 19

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2 ( ) 2 ( d ) 19

22) Two vibrating strings o the same material but lengths L and 2L have radii 2r and r

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22) Two vibrating strings o the same material but lengths L and 2L have radii 2r and r respectively. They are st etched under the same tension. Both the strings vibrate in their

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respectively. They are st etched under the same tension. Both the strings vibrate in their fundamental mode , the one of length L with frequency

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fundamental mode , the one of length L with frequency

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1

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1

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2

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2 is given by

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is given by ( a ) 2 ( b ) ( c ) 8 ( d ) 1

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( a ) 2 ( b ) ( c ) 8 ( d ) 1

23 ) Two monoatomic ideal gases 1 and 2 of molecular masses m

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23 ) Two monoatomic ideal gases 1 and 2 of molecular masses menclosed in separate containers kept at the same temperature. Te ratio of the speed of

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enclosed in separate containers kept at the same temperature. Te ratio of the speed of sound in gas 1 to that in gas 2 is given by

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sound in gas 1 to that in gas 2 is given by

( a )

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( a )

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1

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1m

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mm

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m

24 ) The ratio of the speed of sound in nitrogen gas to that in helium gas at 300 K is www.

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24 ) The ratio of the speed of sound in nitrogen gas to that in helium gas at 300 K is

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26 ) Y ( x, t ) = ]5 )5t 4x ([

8.02 represents a moving pulse where x and y are n metres

and t in second. Then ( a ) pulse is moving positive X-direction ( b ) in 2 s it will travel a distance of 2.5 m ( c ) its maximum displacement is 0.16 m ( d ) it is a symmetric pulse [ IIT 1999 ] 27 ) In a wave motion y = A sin ( kx - t ), y can represent ( a ) electric field ( b ) magnetic field ( c ) displacement ( d ) pressure [ IIT 1999 ]

28 ) Standing waves can be produced ( a ) on a string clamped at both ends ( b ) on a string clamped at one end and free at the other ( c ) when incident wave gets reflected from a wall ( d ) when two identical waves with a phase difference of are moving in the same direction [ IIT 1999 ]

29 ) In hydrogen spectrum, the wavelength of H ne is 656 nm, whereas in the spectrum of a distant galaxy, H line wavelength is 706 nm. Estimated speed of galaxy with respect to earth is

( a ) 2x10^8 m s ( b ) 2x10^7 m s ( c ) 2x10^6 m / s ( d ) 2x10^5 m / s [ IIT 1999 ] 30 ) A string of length 0.4 m and mass 0.01 kg is tightly clamped at its ends. The tension

in the string is 1.6 N. Identica wave pulses are produced at one end at equal intervals of time t, which allows constructive interference between successive pulses is

( a ) 0.05 s ( b ) 0.10 s ( c ) 0.20 s ( d ) 0.40 s [ IIT 1998 ]

31 ) The ( x, y ) coordinates f the corners of a square plate are ( 0, 0 ), ( L, 0 ), ( L, L ) and ( 0, L ). The edges of the plate are clamped and transverse standing waves are set up in it. If u ( x, y ) denotes the displacement of the plate at the point ( x, y ) at some instant of t me, the possible expression ( s ) for u is ( are ) ( a = positive constant )

( a ) a cos 2L

x cos

2Ly ( b ) a sin

Lx

sin

Ly

( c ) a sin Lx sin

Ly2 ( d ) a cos

Lx2 sin

Ly [ IIT 1998 ]

32 ) A transverse sinusoidal wave of amplitude a, wavelength and frequency f is travelling on a stretched string. The maximum speed of any point on the string is v / 10, where v is the speed of propagation of the wave. If a = 0.001 m and v = 10 m / s, then and f are given by

( a ) = 2 10 2 m ( b ) = 10 3 m ( c ) f =

2103 Hz ( d ) f = 104 Hz [ IIT 1998 ]

33 ) A traveling wave in a stretched string is described by the equation y = A sin ( kx - t ). The maximum particle velocity is

( a ) A ( b ) / k ( c ) d / dk ( d ) x [ IIT 1997 ]

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.com ( d ) it is a symmetric pulse [ IIT 1999 ]

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( c ) displacement ( d ) pressure [ IIT 1999 ]

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( c ) displacement ( d ) pressure [ IIT 1999 ]

( b ) on a string clamped at one end and free at the other

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( b ) on a string clamped at one end and free at the other ( c ) when incident wave gets reflected from a wall

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( c ) when incident wave gets reflected from a wall ( d ) when two identical waves with a phase difference of

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( d ) when two identical waves with a phase difference of are moving in the same direction

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are moving in the same direction

29 ) In hydrogen spectrum, the wavelength of H

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29 ) In hydrogen spectrum, the wavelength of H

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ne is 656 nm, whereas in the spectrum of

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ne is 656 nm, whereas in the spectrum of line wavelength is 706 nm. Estimated speed of galaxy with respect

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line wavelength is 706 nm. Estimated speed of galaxy with respect

s ( b ) 2x10^7 m

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s ( b ) 2x10^7 m

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s ( c ) 2x10^6 m

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s ( c ) 2x10^6 m s ( c ) 2x10^6 m

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s ( c ) 2x10^6 m

30 ) A string of length 0.4 m and mass 0.01 kg is tightly clamped at its ends. The tension

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30 ) A string of length 0.4 m and mass 0.01 kg is tightly clamped at its ends. The tension in the string is 1.6 N. Identica wave pulses are produced at one end at equal intervals

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in the string is 1.6 N. Identica wave pulses are produced at one end at equal intervals t, which allows constructive interference between successive pulses is

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t, which allows constructive interference between successive pulses is ( a ) 0.05 s ( b ) 0.10 s ( c ) 0.20 s ( d ) 0.40 s

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( a ) 0.05 s ( b ) 0.10 s ( c ) 0.20 s ( d ) 0.40 s

31 ) The ( x, y ) coordinates f the corners of a

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31 ) The ( x, y ) coordinates f the corners of a ( 0, L ). The edges of the plate are clamped and transverse standing waves are set up

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( 0, L ). The edges of the plate are clamped and transverse standing waves are set up in it. If u ( x, y ) denotes the displacement of the plate at the point ( x, y ) at some

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in it. If u ( x, y ) denotes the displacement of the plate at the point ( x, y ) at some instant of t me, the possible expression ( s ) for u is ( are ) ( a = positive constant )

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instant of t me, the possible expression ( s ) for u is ( are ) ( a = positive constant )

( a ) a cos

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( a ) a cos

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2L

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2Lx

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x

( c ) a sin

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( c ) a sin

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32 ) A transverse sinusoidal wave of amplitude a, wavelength www.

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32 ) A transverse sinusoidal wave of amplitude a, wavelength on a stretched string. The maximum speed of any point on the string is v ww

w.ex

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on a stretched string. The maximum speed of any point on the string is v


34 ) A whistle giving out 450 Hz approaches a stationary observer at a speed of 33 m s. The frequency heard by the observer in Hz is

( a ) 409 ( b ) 429 ( c ) 517 ( d ) 500 [ IIT 1997 ]

35 ) The extension in a string, obeying Hookes law is X. The speed of sound in the stretched string is V. If the extension in the string is increased to 1.5 X, t e speed of sound will be

( a ) 1.22 V ( b ) 0.61 V ( c ) 1.50 V ( d ) 0.75 V [ IIT 1996 ]

36) An open pipe is suddenly closed at one end with the result th t the frequency of third harmonic of the closed pipe is found to be higher by 100 Hz than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is

( a ) 200 Hz ( b ) 300 Hz ( c ) 240 Hz ( d ) 480 Hz [ IIT 1996 ]

37 ) The displacement y of a particle executing periodic motion s given by

y = 4 cos2 t 21 sin ( 1000t ).

The expression may be considered to be a res lt of the superposition of _______ independent harmonic motions.

( a ) two ( b ) three ( c ) four ( ) ive [ IIT 1992 ]

38 ) Two identical straight wires are stretc ed so as to produce 6 beats per second when vibrating simultaneously. On cha ing the tension slightly in one of them, the beat frequency remains unchanged. Deno ing by T1, T2, the higher and the lower initial tensions in the strings, it co ld b said that while making the above changes in tension

( a ) T2 was decreased ( b ) T1 was increased ( c ) T2 was increased ( d ) T1 was decreased [ IIT 1991 ]

39 ) A wave is represented by the equation y = A sin ( 10 x + 15 t + 3 ), where x is in metres and t is n seconds. The expression represents

( a ) a wave traveling n the positive x-direction with a velocity 1.5 m s ( b ) a wave traveling in the negative x-direction with a velocity 1.5 m / s ( c ) a wave traveling in the negative x-direction having a wavelength 0.2 m ( d ) a wave raveling in the positive x-direction having a wavelength 0.2 m [ IIT 1990 ]

40 ) Velocity o sound in air 320 m / s. A pipe closed at one end has a length of 1 m. Neglecting end corrections, the air column in the pipe can resonate for sound of freque cy

( a ) 80 Hz ( b ) 240 Hz ( c ) 320 Hz ( d ) 400 Hz [ IIT 1989 ]

41 ) A wave represented by the equation y = a cos ( kx - t ) is superposed with another wave to form a stationary wave such that the point x = 0 is a node. The equation for the other wave is

( a ) a sin ( kx + t ) ( b ) - a cos ( kx - t ) ( c ) - a cos ( kx + t ) ( d ) - a sin ( kx - t ) [ IIT 1988 ] 42 ) An organ pipe P1, closed at one end and vibrating in its first harmonic, and another

pipe P2, open at both ends and vibrating in its third harmonic, are in resonance with a given tuning fork. The ratio of the length of P1 to that of P2 is

( a ) 38 ( b )

83 ( c )

21 ( d )

31 [ IIT 1988 ]

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[ IIT 1997 ]

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[ IIT 1997 ]

35 ) The extension in a string, obeying Hookes law is X. The speed of sound in the

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.com35 ) The extension in a string, obeying Hookes law is X. The speed of sound in the stretched string is V. If the extension in the string is increased to 1.5 X, t e speed of

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.comstretched string is V. If the extension in the string is increased to 1.5 X, t e speed of ( a ) 1.22 V ( b ) 0.61 V ( c ) 1.50 V ( d ) 0.75 V

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.com ( a ) 1.22 V ( b ) 0.61 V ( c ) 1.50 V ( d ) 0.75 V [ IIT 1996 ]

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36) An open pipe is suddenly closed at one end with the result th t the frequency of third

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36) An open pipe is suddenly closed at one end with the result th t the frequency of third be higher by 100 Hz than the fundamental

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be higher by 100 Hz than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is

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frequency of the open pipe. The fundamental frequency of the open pipe is ( a ) 200 Hz ( b ) 300 Hz ( c ) 240 Hz ( d ) 480 Hz

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( a ) 200 Hz ( b ) 300 Hz ( c ) 240 Hz ( d ) 480 Hz

37 ) The displacement y of a particle e ecuting periodic motion s given by

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37 ) The displacement y of a particle e ecuting periodic motion s given by

The expression may be considered to be a res lt of the superposition of _______

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The expression may be considered to be a res lt of the superposition of _______

( a ) two ( b ) three ( c ) four ( ) ive

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( a ) two ( b ) three ( c ) four ( ) ive

38 ) Two identical straight wires are stretc ed so as to produce 6 beats per second when

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38 ) Two identical straight wires are stretc ed so as to produce 6 beats per second when vibrating simultaneously. On cha ing the tension slightly in one of them, the beat

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vibrating simultaneously. On cha ing the tension slightly in one of them, the beat frequency remains unchanged. Deno ing by T

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frequency remains unchanged. Deno ing by Ttensions in the strings, it co ld b said

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tensions in the strings, it co ld b said

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was decreased ( b ) T

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was decreased ( b ) T1

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1 was increased

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was increased was increased ( d ) T

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was increased ( d ) T

39 ) A wave is represented by the equation y = A sin ( 10

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39 ) A wave is represented by the equation y = A sin ( 10 metres and t is n seconds. The expression represents

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metres and t is n seconds. The expression represents ( a ) a wave traveling n the positive x-direction with a velocity 1.5 m

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( a ) a wave traveling n the positive x-direction with a velocity 1.5 m ( b ) a wave traveling in the negative x-direction with a velocity 1.5 m

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( b ) a wave traveling in the negative x-direction with a velocity 1.5 m

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( c ) a wave traveling in the negative x-direction having a wavelength 0.2 m

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( c ) a wave traveling in the negative x-direction having a wavelength 0.2 m ( d ) a wave raveling in the positive x-direction having a wavelength 0.2 m [ IT 1990 ]

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( d ) a wave raveling in the positive x-direction having a wavelength 0.2 m [ IT 1990 ]

40 ) Velocity o sound in air 320 m

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40 ) Velocity o sound in air 320 m Neglecting end corrections, the air column in the pipe can resonate for sound of

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Neglecting end corrections, the air column in the pipe can resonate for sound of

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freque cy

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freque cy ( a ) 80 Hz ( b ) 240 Hz ( c ) 320 Hz ( d ) 400 Hz

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( a ) 80 Hz ( b ) 240 Hz ( c ) 320 Hz ( d ) 400 Hz

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41 ) A wave represented by the equation y = a cos ( kx


43 ) The displacement of particles in a string stretched in the x-direction is represented by y. Among the following expressions for y, those describing wave motion are

( a ) cos kx sin t ( b ) k2x2 - 2t2 ( c ) cos2 ( kx + t ) ( d ) cos ( k2x2 - 2t2 ) [ IIT 1987 ] 44 ) A tube closed at one end and containing air produces, when excited, the fundamental

note of frequency 512 Hz. If the tube is open at both ends the fundam ntal frequency that can be excited is ( in Hz )

( a ) 1024 ( b ) 512 ( c ) 256 ( d ) 128 [ IIT 1986 ]

45 ) An air column in a pipe which is closed at one end, wil be in resonance with a vibrating tuning fork of frequency 264 Hz if the length of the column in cm is

( a ) 31.25 ( b ) 62.50 ( c ) 93.75 ( d ) 125 [ IIT 1985 ]

46 ) A transverse wave is described by the equation = 0 sin 2 ( ft - x / ). The maximum particle velocity is equal to four times he wave velocity if

( a ) =4Y0 ( b ) =

2Y0 ( c ) 0Y ( d ) 2 0Y [ IIT 1984 ]

47 ) A wave equation which gives the displac ment along the y-direction is given by y = 10 4 sin ( 60t + 2x ) where x and y re in metres and t is time in seconds. This represents a wave

( a ) traveling with a velocity of 30 m / s in the negative x-direction ( b ) of wavelength m ( c ) of frequency 30 / H ( d ) of amplitude 10 4 m tr vel ng along the negative x-direction [ IIT 1982 ]

48 ) A cylindrical tube, pen at both ends, has a fundamental frequency f in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now

( a ) 2f ( b )

2f3 ( c ) f ( d ) 2f [ IIT 1981 ]

Answers

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 d c b b b c d c a c c a c d b b b a c b d

22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 d b c a,c,d b,c,d all a,b,c b b b,c a,c a d a a b c,d b,c a,b,d

41 42 43 44 45 46 47 48 c b a a a,c b a,b,c,d c

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) [ IIT 1987 ]

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) [ IIT 1987 ]

44 ) A tube closed at one end and containing air produces, when excited, the fundamental

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.com44 ) A tube closed at one end and containing air produces, when excited, the fundamental note of frequency 512 Hz. If the tube is open at both ends the fundam ntal frequency

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.comnote of frequency 512 Hz. If the tube is open at both ends the fundam ntal frequency ( a ) 1024 ( b ) 512 ( c ) 256 ( d ) 128

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.com ( a ) 1024 ( b ) 512 ( c ) 256 ( d ) 128 [ IIT 1986 ]

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45 ) An air column in a pipe which is closed at one end, wil be in resonance with a

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45 ) An air column in a pipe which is closed at one end, wil be in resonance with a the length of the column in cm is

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the length of the column in cm is ( a ) 31.25 ( b ) 62.50 ( c ) 93.75 ( d ) 125

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( a ) 31.25 ( b ) 62.50 ( c ) 93.75 ( d ) 125

46 ) A transverse wave is described by the equation =

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46 ) A transverse wave is described by the equation = 0

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0 sin 2

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sin 2 four times he wave velocity if

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four times he wave velocity if

( c )

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( c ) 0

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0Y

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Y

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( d ) 2

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( d ) 2

47 ) A wave equation which gives the displac ment along the y-direction is given by

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47 ) A wave equation which gives the displac ment along the y-direction is given by sin ( 60t + 2x ) where x and y re in metres and t is time in seconds. This

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sin ( 60t + 2x ) where x and y re in metres and t is time in seconds. This

( a ) traveling with a velocity of 30 m

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( a ) traveling with a velocity of 30 m /

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/

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s in the negative x-direction

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s in the negative x-direction s in the negative x-direction

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s in the negative x-direction

H

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H 4

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4 m tr vel ng along the negative x-direction [ IIT 1982 ]

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m tr vel ng along the negative x-direction [ IIT 1982 ]

48 ) A cylindrical tube, pen at both ends, has a fundamental frequency f in air. The tube is

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48 ) A cylindrical tube, pen at both ends, has a fundamental frequency f in air. The tube is dipped vertically in water so that half of it

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dipped vertically in water so that half of it air-column is now

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air-column is now

( b )

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( b )

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2

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2f3

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f3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 www.

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 www.

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d c b b b c d c a c c a c d b b b a c b d www.

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d c b b b c d c a c c a c d b b b a c b d www.

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22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 www.

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22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 www.

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