Transverse or longitudinal waves transport energy from one point to another. Each particle in the medium vibrates or oscillates, and disturbs the neighbouring.

Transverse or longitudinal waves transport energy from one point to another. Each particle in the medium vibrates or oscillates, and disturbs the neighbouring particles in a ‘domino-like’ effect.

What happens when two waves meet at a point? How does the particle of the medium react at that point?

Wave Phenomena1

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Chapter 17: Wave Phenomena

Ripple Tank

The basic component is a large transparent tray and a bar suspended by elastic bands and attached to a motor. The motor vibrates the bar to create waves on the surface of the water. The frequency of the wave is determined by the motor.


When a series of waves form on the surface of the water, the crests act as lenses that focus the light rays to form bright lines on the screen.

Dark lines Troughs Bright lines Crests.


The distance between the dark lines or the distance between the bright lines is equal to the wavelength of the wave train on the water surface.

A circular wave has circular wave fronts that expand outward.

It is made up of wave trains moving outwards from a single point.

Image of wave pattern

A plane wave has parallel wave fronts that have constant wavelength and amplitude.

It is made up of similar wave trains moving in the same direction.

A plane wave - wave trains travelling side by side

Crest

Direction of wave motion


Plane Wave

Circular Wave

Reflection

The angle between the direction of motion of the incident wave and the normal is called the angle of incidence, i.

The angle between the direction of motion of the reflected wave and the normal is called the angle of reflection, r.


A wave can be ‘bounced’ off the surface of an obstacle or barrier.

The incoming wave is called the incident wave and the ‘bounced’ off wave is called the reflected wave.

angle of incidence = angle of reflection

The following diagrams show how a circular wave front from a point source (S1) is reflected off a plane surface.

The reflected wave front seems to come from another point source (S2) behind the reflected surface.

A circular wave front being reflected off a flat surface.

(a) (b)

(c) (d)

S1 . S2 . S1 . S2 .

S1 . S2 . S1 . S2 .


Refraction is caused by the change in the speed of a wave when it travels from one medium to another.

Water waves slow down when they travel into shallower regions. The frequency does not change. Only the wavelength is affected by the change in speed.


Refraction

If the block is angled such that neighbouring wave trains do not cross into the shallower region at the same time, we will observe the wave bending towards the normal.

The normal is the line perpendicular to the line separating the regions of different depths.

The angle between the direction of motion of the incident wave and the normal is called the angle of incidence i

The angle between the direction of motion of the refracted wave and the normal is called the angle of refraction r.

sin i / sin r = vi / vr = λi / λr

wherei is the angle of incidence,r is the angle of refraction,vi is the speed of the incident wave,vr is the speed of the refracted wave,λi is the wavelength of the incident wave andλr is the wavelength of the refracted wave.


Diffraction

When a wave passes the edge of an obstacle, it spreads out from its original direction of motion. This phenomenon is called the diffraction of waves.

The bending of waves is more pronounced when the size of the obstacle is comparable to the size of the wavelength.

Diffraction of waves is more pronounced when the opening is comparable to the wavelength.


Spreading of water waves around the edge of an obstacle in a ripple tank

Wooden bar of a ripple tank

Obstacle Wave front bending away from original direction


Superposition of waves is the addition of the amplitudes of two or more waves that meet at a point.

When waves move through a medium, the particles react by oscillating about their equilibrium position.

When two or more waves meet at a point, the particles at that point oscillate corresponding to the resultant of the waves’ amplitudes.

Superposition of waves

(a) Two pulses of the same amplitude, A, approacheach other along the same medium.

(b) When they meet, they combine to form a resultant amplitude.

(c) In this instance, they combine to form an amplitude that is twice the individual amplitudes. (A + A = 2A).

(d) The pulses pass each other with their original amplitudes.

Superposition of approaching waves of same amplitude


Interference

When waves of similar wavelength, amplitudes and frequency meet, they form an interference pattern due to the superposition of waves.


Coherent waves

The diagram shows waves produced by coherent sources. Waves produced by coherent sources are generated in phase, and have the same frequency and wavelength.

Coherent sources produce well-defined interference patterns.

The black dotted lines are called anti-nodal lines. The red dotted lines are the nodal lines.

The anti-nodal line is where constructive interference occurs (the waves that meet at those points are in phase).

The nodal line is where destructive interference occurs (the waves that meet at those points are out of phase).


Constructive interference displays maximum change in amplitudesDestructive interference displays minimal or no change in amplitudes.

(a) Waves from S1 and S2 arrive at point X in

phase. Each wave has amplitude of A. When they meet, they combine to form resultant amplitude.

(b) The resultant amplitude to the two sources fluctuates from 2A to (−2A).

t

t

t

S1

S2

X

Constructive interference

(a) Waves from S1 and S2 arrive at point Y out of

phase. Wave S1 has amplitude of A and Wave S2

has amplitude of (−A) at point Y. When they meet, they combine to form resultant amplitude of zero.

(b)The resultant amplitude of the two sources is zero.

t

t

t

S1

S2

Y


Destructive interference

Young’s Double Slit Experiment

Thomas Young demonstrated the idea of interference using the double slit experiment.

Two coherent light sources were used to produce an interference pattern.


• A monochromatic light source is used.

• A small slit S3 is used to diffract light and simulate a point source. Light rays from S3 enter slits S1 and S2, and simulate two more point sources.

• The diffracted waves from these two simulated points overlap and superimpose to form an interference pattern.

Constructive interference occurs along the anti-nodal lines. In Young’s double slit experiment, the path difference of the points along this line from the two sources is equal to 1 λ, 2 λ, 3 λ and so on.

Destructive interference occurs along the nodal lines. In Young’s double slit experiment, the path difference of the points along this line from the two sources is equal to 0.5 λ, 1.5 λ, 2.5 λ and so on.


(a) An interference fringe pattern from a Young’s double slit experiment. Note the positions of the anti-nodal lines.

(b) More fringes appear when the wavelength is decreased. Note that the anti-nodal lines are closer together.

(c) More fringes also appear when the slit separation is increased. Note that the anti-nodal lines are closer together.

How slit separation and wavelength affects the interference fringe pattern:


Transverse or longitudinal waves transport energy from one point to another. Each particle in the medium vibrates or oscillates, and disturbs the neighbouring.

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