# 8.2.2 Interference & Coherence

### Interference & Coherence

• Interference occurs when waves overlap and their resultant displacement is the sum of the displacement of each wave
• This result is based on the principle of superposition and the resultant waves may be smaller or larger than either of the two individual waves
• Interference of two waves can either be:
• In phase, causing constructive interference. The peaks and troughs line up on both waves. The resultant wave has double the amplitude
• In anti-phase, causing destructive interference. The peaks on one wave line up with the troughs of the other. The resultant wave has no amplitude

Waves in superposition can undergo constructive or destructive interference

• At points where the two waves are neither in phase nor in antiphase, the resultant amplitude is somewhere in between the two extremes
• Waves are coherent if they have the same frequency and constant phase difference

Coherent v non-coherent wave. The abrupt change in phase creates an inconsistent phase difference

• Coherence is vital in order to produce an observable interference pattern
• Laser light is an example of a coherent light source, whereas filament lamps produce incoherent light waves

#### Worked example

• At point X:
• Both peaks of the waves are overlapping. This is constructive interference and rules out options C and D
• At point Y:
• Both troughs are overlapping and there constructive interference occurs
• At point Z:
• A peak of one of the waves meets the trough of the other. This is destructive interference (Row B)

#### Exam Tip

Think of ‘constructive’ interference as ‘building’ the wave and ‘destructive’ interference as ‘destroying’ the wave

### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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