Episode 320: Superposition

This episode introduces the basic idea of superposition of waves, explaining what happens when two or more waves meet.

Summary

  • Discussion: Recapping wave ideas (10 minutes)
  • Demonstration: Waves on a rope (15 minutes)
  • Discussion: Ripples on a pool (10 minutes)
  • Student questions: Adding waves graphically (30 minutes)

Discussion: Recapping wave ideas
Show a representation of a wave and rehearse basic knowledge about waves:

Frequency f is determined by the source of the waves (the “transmitter”)

Wave speed c is determined by the medium in or on which the wave propagates.

So wavelength follows from c = fλ 

At boundaries (reflection, refraction etc), f must stay the same.

Demonstration: Waves on a rope etc
This is a useful attention grabber. Pass pulses through each other on a stretched rope, rubber tube or stick wave machine.

Set off a large amplitude pulse; just before the first pulse is reflected, chase it with a smaller amplitude pulse – observe that the pulses briefly combine then pass through each other, and carry on as before.

(For later comment, observe and note the phase change on reflection; that is, the pulse turns upside down when it reflects.)

Draw attention to this ‘damage-less collision’ of waves passing through each other that is a hallmark of all wave behaviour. Colliding particles rebound and may suffer damage. [The other hallmark of wave motion is that the speed of a wave is constant and determined by the medium supporting the wave motion. Unlike particles, ‘friction’ doesn’t reduce the speed; it reduces the energy (i.e. the amplitude) of the wave.]

When two waves arrive at the same point and at the same time, the resultant displacement is given by the algebraic sum of the two individual displacements. (‘Algebraic sum’ means that you have to take account of positive and negative values.)

Ripples on a pool

Discussion: Ripples on a pool
Superposition is an everyday phenomenon. Show some images of ripples on a pool of water as they pass through each other.

Episode 320-1: Overlapping ripples (Word, 322 KB)

Student questions: Adding waves graphically
Drawing exercises reinforce the idea that, to find the displacement when two waves meet, you simply calculate the algebraic sum of the two individual displacements.

Episode 320-2: Phase difference and superposition (Word, 94 KB)

Episode 320-3: Superposition of waves: a drawing exercise (Word, 60 KB)

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Episode 320: Superposition (Word, 506 KB)