Superposition and Coherence

Principle of superposition

When two or more waves cross, the resultant displacement equals the vector sum of the individual displacements

Interference

The effect when two or more waves superpose with each other

Constructive interference

When the peak and peak or trough and trough combine to give a bigger peak or trough

Destructive interference

The displacements from a peak and a trough cancel each other out to a smaller displacement

Total destructive interference

The peak and trough are equal in size and have a vector sum of 0

In phase

Points on a wave are at the same point in the wave cycle

How do you know if a point is in phase

Points in phase will have the same displacement and velocity

Out of phase

Points that are not at the same point in the wave cycle

What is one complete wave cycle in degrees

360°

What is one complete wave cycle in radians

2π radians

Exactly out of phase

Points with a phase difference of odd number multiples of 180°

When do in phase waves usually occur

Waves coming from the same oscillator

When will waves have wavefronts

The waves are coherent, in phase and travelling in the same direction

Wavefronts

Imaginary points, cutting across all the waves, joining up all the points that are in phase with each other

How to find wavelength using wavefronts

Distance between each wavefront

What condition must be met to get interference patterns

Waves must be coherent

Coherent sources

Same wavelength and frequency, with a fixed phase difference between them

Path difference

The amount by which the path travelled by one wave is longer than the path travelled by the other wave

What does interference being constructive or destructive depend on

How much further one wave has travelled to get to that point

When does constructive interference occur (path difference)

The path difference is a whole number of wavelengths

When does destructive interference occur (path difference)

The path difference is an odd number of half wavelengths

How do you know if two points are in phase by phase difference

Phase difference is 0 or a multiple of 360°

Experiment to investigate the interference of sound waves

1- Connect two speakers to the same oscillator

2- Walk slowly across the room in front of them

3- You should hear varying volumes of sound, dependent on path difference

Why should the two speakers be connected to the same oscillator in the interference experiment

So that the sound waves are coherent and in phase