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
Constructive & Destructive Interference
- Constructive interference occurs when the waves superpose and have displacements in the same direction (both positive or both negative)
- Destructive interference occurs when the waves superimpose and have displacements in opposite directions (one positive and one negative)
- When two waves with the same amplitude meet at a point, they can:
- Be in phase and interfere constructively, so that the displacement of the resultant wave is double the displacement of each individual wave
- Be in anti-phase and interfere destructively, so that the displacement of the resultant wave is equal to zero
Waves in superposition can undergo constructive or destructive interference
- 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
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.
