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
- The principle of superposition applies to both transverse and longitudinal waves
- Interference occurs whenever two or more waves superpose
- For a clear stationary interference pattern, the waves must be of the same:
- Type
- Amplitude
- Frequency
- They must also have a constant phase difference
- Superposition occurs for any two waves or pulses that overlap, and can result in a mix of constructive and destructive interference
- For example, the peak of one wave superposes with the peak of another wave with a smaller displacement
- The resultant peak will have a displacement that is in the middle of the displacement of both waves
- Superposition can also be demonstrated with two pulses
- When the pulses meet, the resultant displacement is the algebraic sum of the displacement of the individual pulses
- After the pulses have interacted, they then carry on as normal
Superposition of pulses
When two pulses superimpose their effects can be combined at the point where the peaks of troughs meet
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
- Each square on the y-axis represents 0.2
Examiner 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.
