Waves• Energy can be transported by

transfer of matter. For example by a thrown object.

• Energy can also be transported by wave motion without the transfer of matter. For example by sound waves and electromagnetic waves.

Waves• Mechanical waves travel through

matter. The matter is referred to as a “medium”. Examples are sound eaves, waves on a string, and waves on water.

• Electromagnetic waves do not require a medium through which to travel. Examples are gamma rays, x-rays, ultraviolet light visible light etc.

Waves• A wave is a disturbance or oscillation

that travels through matter or space, accompanied by a transfer of energy.

WavesA transverse wave causes the medium particles to vibrate in the direction perpendicular to the motion of the wave.

Waves

A longitudinal wave causes the medium particles to vibrate in the direction parallel to the motion of the wave.

Waves

A pulse is a single disturbance travelling through a medium or space.

Figure 14-7A Reflected Wave Pulse: Fixed End

Figure 14-8A Reflected Wave Pulse: Free End

A crest is the point on a wave with the maximum value of upward displacement within a cycle.

A trough is the point on a wave with the minimum value of downward displacement within a cycle.

The amplitude is the value of the maximum or the minimum displacement from the average position

The wavelength (l) is the distance between corresponding

points on consecutive waves.Unit: m

The frequency (f) is the number of waves that pass a given point per

unit time.Unit: Hz=s-1

The speed of a wave is given by v=fl

Unit: m/s

Figure 14-1A Wave on a String

Waves

A standing wave oscillates with time but appears to be fixed in its location

Figure 14-19Wave superposition occurs when two or more waves meet in the same medium. The principle of superposition states that at the point where

two or more waves meet the displacement of the medium equals the sum of the displacements of the individual waves.

Figure 14-20

The effect of two or more waves travelling through a medium is called interference.

Constructive interference

Destructive interference

Figure 14-20Nodes and antinodes

• Nodes occur at points where two waves interact in such a way that the medium remains undisturbed.

• Antinodes occur at points where two waves interact in such a way that maximum displacement of the medium occurs.

Figure 14-20Nodes and antinodes

NodeAntinode

Figure 14-20Nodes and antinodes

• If one end of a string is attached to a vibrating object, and the other end is fixed, two wave trains are produced. One by the incident vibration, and one by reflection from the fixed end. The reflected wave train returns to the source and is reflected again. If the second reflection is in phase with the source, constructive and destructive interference will produce stationary antinodes and nodes. The string will appear to be vibrating in segments.

Figure 14-20Nodes and antinodes

• This is called a standing wave an is an example of resonance.

String fixed at both ends

Figure 14-24bHarmonics

Figure 14-24cHarmonics

Reflection of Waves• When a wave train strikes a barrier it is

reflected. • The law of reflection states that the angle

of incidence is equal to the angle of reflection.• The direction of the wave train’s travel is

called a ray, and the angles are measured from the normal to the boundary.

Reflection

Refraction of Waves• When a wave train moves from one

medium to another, its velocity changes.• Since the waves in the new medium are

produced by the waves in the old medium, their frequency remains the same. Since the velocity changes, but not the frequency, the wavelength must change.

Refraction of Waves• When parallel waves approach a

boundary between media along the normal, their direction does not change.• When parallel waves approach a

boundary between media at an angle to the normal, their direction is changed. This phenomenon is called refraction.

Refraction of Waves• When parallel waves approach a

boundary between media along the normal, their direction does not change.• When parallel waves approach a

boundary between media at an angle to the normal, their direction is changed. This phenomenon is called refraction.

Boundary

Refraction of Waves

Boundary

Refraction of Waves

Diffraction of Waves• Diffraction is the bending of waves

around obstacles in their path.

Diffraction of Waves

Diffraction of Waves

Diffraction of Waves• An interference pattern can be

created by placing a barrier with two openings in front of a wave train.• The openings must be smaller than

the wavelength of the approaching wave train.

Diffraction of Waves• In regions where crests overlap with crests, and

troughs overlap with troughs, constructive interference occurs, and antinodes lie along those lines. These lines are called antinodal lines.• In regions where crests overlap with troughs

destructive interference occurs, and the medium is undisturbed. These lines are called nodal lines.

Diffraction of Waves• The pattern produced is called an

interference pattern.• Different wavelengths produce similar

interference patterns, but the nodal and antinodal lines are in different places.• Regardless of wavelength a central

antinodal line always falls in the center of the pattern.

Standing waves on a string –

In order for standing waves to form on a string, the length of the string L must be a multiple of one

half the wavelength

1, 2,3...2

L n nl

String fixed at both ends

2Ll

Figure 14-24bHarmonics

Ll

Figure 14-24cHarmonics

23Ll

v= =

F masslength

F the tension in the string

Speed of waves on a string

A 4.0 m length of string has a mass of 20.00g. It is stretced between two points, and experiences a tension of 40.0N. The string is plucked.a) What is the velocity of a wave on the string?b)Wha

Example

t is the longest wavelength possible for a standing wave on the string?c) What is the frequency of the longest wavelength possible for a standing wave on the string?

Speed of waves on a string

3

3

0.02000kg) = 5.00 104.0

40.0v= = =89.445.00 10

Solutionmass kgalength m m

F N mkg sm

Speed of waves on a string

)Longest wavelength possible is =2L=2 4.0 8.0

88.44) 11.055

8.0

Solutionb

m mm

v sc v f f Hzm

ll

ll

Speed of waves on a string