The principle of superposition
- When two or more waves arrive at the same point and overlap, their amplitudes combine
- This is called superposition
- The principle of superposition states that:
When two or more waves overlap at a point, the displacement at that point is equal to the sum of the displacements of the individual waves
- The superposition of surface water waves shows the effect of this overlap
- There are areas of zero displacement, where the water is flat
- There are areas of increased displacement, where the water waves are higher
The dogs make waves in the water which superimpose to give areas of both zero and increased displacement.
- It is possible to analyse superposition clearly when the waves are drawn on a vertical displacement (amplitude)-displacement graph
Waves can superimpose so their amplitudes are added together often creating a larger resultant amplitude
- Interference is the effect of this overlap
- This is explained in the next Interference & coherence
- Individual wave displacements may be positive or negative and are combined in the same way as other vector quantities
- It is possible to analyse superposition clearly when the waves are drawn on a displacement-time graph
- Superposition can also be demonstrated with two pulses
- When the pulses meet, the resultant displacement is also the algebraic sum of the displacement of the individual pulses
- After the pulses have interacted, they then carry on as normal
When two pulses overlap their displacements combine to form a resultant displacement
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.
