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Wize University Physics Textbook (Master) > Waves: Mechanical

Principals of Superposition: Waves

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Interference and Superposition



The overlapping of waves is called interference. They combine as they pass through each other while traveling in the medium.


Principle of Superposition: When two waves overlap, the actual displacement of any particle in the medium is the algebraic sum of their displacement due to each wave if only that wave were present:
y(x,t)=y1(x,t)+y2(x,t)y\left(x,t\right)=y_1\left(x,t\right)+y_2\left(x,t\right)

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Wize Concept
  • Crest meets crest, or trough meets trough: we have constructive interference (amplitude gets twice as big)
  • Crest meets trough: we have destructive interference (amplitudes cancel out)



Wize Tip
When adding to waves, add their displacements together.


Example: Superposition


Two waves approach each other, both moving at speed of 11 m/s. What happens at t=4t = 4 s?



After 4 seconds of moving towards each other, the waves will overlap like this:


For each time value, add the amplitudes of the two waves. The superposition will look like this:



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Practice: Superposition

You have a snapshot of two waves on a string as shown below, at t=0t = 0s . They are moving towards each other.

The wave on the left is moving at +2.0+ 2.0 m/s. The wave on the right is moving at −1.0-1.0 m/s. Sketch what happens at t=2t = 2s.