The Principle of Superposition
- The principle of superposition states that:
When two or more waves meet, the resultant displacement is the vector sum of the displacements of the individual waves
- This principle describes how waves which meet at a point in space interact
- When two waves with the same frequency and amplitude arrive at a point, they superpose either:
- in phase, causing constructive interference. The peaks and troughs line up on both waves. The resultant wave has double the amplitude
- or, 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
Constructive and destructive interference
Waves in superposition can undergo constructive or destructive interference
- The principle of superposition applies to all types of waves i.e. transverse and longitudinal
Worked example
Two overlapping waves of the same types travel in the same direction. The variation with x and y displacement of the wave is shown in the figure below.
Use the principle of superposition to sketch the resultant wave.
Answer:
- The graph of the superposition of both waves is in black:
- To plot the correct amplitude at each point, sum the amplitude of both graphs at that point
- E.g. A point A, each graph has a value of 0.7. Therefore, the same point with the resultant superposition is 2 × 0.7 = 1.4
Exam Tip
The best way to draw the superposition of two waves is to find where the superimposed wave has its maximum and minimum amplitudes. It is then a case of joining them up to form the wave. Where the waves intersect determines how much constructive or destructive interference will occur.
