This modelling work, which I have spent most of my weekend developing, stems from a very simple question which came up in my AS physics textbook, on the topic of wave interference. It went something along the lines of "Draw 6 diagrams, 1 second apart, to show how these two approaching waveforms interfere". I was surprised at how difficult it was to faithfully do this, even with two simple waveforms in wide discrete time jumps and it got me thinking - how could I use a computer to do this better? The result is in an 8-page investigation, where I have endeavoured to develop some theory about how to model passing and reflecting waves and how they interfere - it begins easy, with some simple linear interference by summation of instantaneous displacements, but soon I found that the mathematics became more complicated (particularly in stage 3, where I began to model how waves slowly escape from a trap, like a solid-state laser but without the quantum stimulated emissions).
I have tried to explain myself fully throughout, although not enough proof-reading has been done to keep it from being a little haphazard, and the last page of the document requires some following-up when I have a little more time. However, I am pretty proud of some of the derivations.
In the paper, I have referenced some equations with numbers in square brackets. These match-up with equations on the corresponding Desmos file (here: http://tinyurl.com/zlmzg9d), to illustrate exactly what each equation looks like in practice.
The paper can be found here: http://tinyurl.com/zwegna4
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