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.
What the sliders mean
- Wave 1: amplitude of wave 1.
- Wave 2: amplitude of wave 2.
- Phase (φ): the phase difference — controls the shift of wave 2 compared to wave 1. It is assumed you have a pretty decent understanding of phase difference already.
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.