2. Introduction
What happens when two waves meet?
Two snooker balls would bounce off one another, but
light behaves differently.
They show behaviour known as interference.
Constructive interference –
two waves on left arrive in
phase (in step).
Resultant wave (bottom left)
has twice the amplitude.
Destructive interference – two
waves on the right arrive out of
phase (out of step).
They cancel each other out.
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3. Interference of sound
Walking around in the space beyond two loudspeakers,
you can hear point where the sound is loud, and point
where it is much softer.
These loud and soft points have a regular pattern.
Your ear receives waves from both speakers.
Suppose the wavelength of the sound waves is 1 m.
If your ear is 4 m from one speaker and 5 m from the
other, there is a path difference of 1 m for the two
waves.
They will be in phase; they interfere constructively and
you hear a loud sound.
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4. Interference of sound
If your ear is 4 m from one speaker and 5.5 m from the
other, the path difference is 1.5 m.
The waves will be out of phase; they will interfere
destructively and you will hear no sound (or a very faint
sound).
• For constructive interference, path difference = nλ
• For destructive interference, path difference
= (n + ½)λ
Interference of other waves
The same effect can be shown for:
1. Ripples – use two dippers attached to a vibrating bar
in a ripple tank.
2. Microwaves – direct the microwaves through two
gaps in a metal plate
3. Light – the ‘Young’s slits’ experiment
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5. Diffraction of ripples
When ripples pass through a gap, they spread out into
the space beyond.
The effect, which is known as diffraction, is greatest
when the width of the gap, x is similar to the
wavelength of the ripples, λ.
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λ = x
Width of gap = x
λ << x
6. Explaining diffraction
When light from lasers is shone through a single slit, a
diffraction pattern of light and dark interference
bands (called ‘fringes’) is seen on the screen.
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We picture waves spreading out from
all pints in the slit
Each point on the screen receives waves from each point
in the slit. These waves interfere.
Where all the interfering waves cancel each other out,
we see a dark fringe (destructive interference)
Where all the interfering waves add up, we see a bright
fringe (constructive interference).
7. Coherent sources
To observe interference patterns when two sets of
waves overlap, they must be coherent.
This means they must have the same wavelength and
frequency; also the phase difference between them
must be constant.
Two loudspeakers are coherent sources.
They are connected to the same signal generator, so
they vibrate back and forth in step with each other.
Light from a lamp is not usually coherent.
It is emitted as photons, and they do not keep in step
with each other.
Laser light is coherent, its photons remain in step
between the source and screen.
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8. Questions
1. What will be observed if two waves, in phase and one
having twice the amplitude of the other, interfere?
2. Draw a ripple diagram to show ripples of wavelength
λ being diffracted by a gap of width 2λ. Draw a
second diagram to show what happens if ripples of
twice this wavelength pass through this same gap.
3. Two dippers are used to produce an interference
pattern in a ripple tank. Are they a pair of coherent
sources? Explain your answer.
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