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Superposition

When two waves meet, the resultant displacement at a point is given by adding their displacements (remember displacement is vector). This is the principle of superposition.

Wave 1: 60
Amplitude of wave 1.
Wave 2: 60
Amplitude of wave 2.
Phase φ: π/2 (90°)
Phase difference between the two waves.
How to read the graph
The resultant (white) is formed by adding the two displacements at each point along the wave. Changing phase shifts how much they reinforce or cancel.

What the sliders mean

Phase difference and interference

Phase difference controls whether the waves reinforce or cancel:

  • In phase: constructive so maximum resultant.
  • In antiphase: destructive so minimum resultant.
  • Anything else: slight reinforcement/cancellation.

In A-level we describe phase difference using fractions of a cycle (p.55 of oxford aqa textbook). The slider just controls the phase difference between wave 1 and 2. I coded it to change the phase of wave 2 because I feel like it makes more sense to move wave 2 and keep wave 1 stationary, though either could move and it would give the same result.

How the model works

Each point on a wave oscillates up and down consistently. I modelled this using a sine wave, which is in accordance with A-level teachings. Please note that this is not reality due to energy losses and distortions from external sources. The displacement depends on:

  • where you are along the wave (position)
  • the point in time

I chose not to include the proper wave equations because it is simply unnecessary - not due to lack of interest. If, like me, you are interested in the further reading, see the wave equation wikipedia. F=ma seems to be everywhere in physics.

Even further reading

Another thing I stumbled across was phasors, which seems to model waves using rotating vectors. I have not yet (03/02/26) explored it because my maths is lacking, but for the more developed reader, see phasors.

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