Let me see: four times five is twelve, and four times six is thirteen, and four times seven is – oh dear! I shall never get to twenty at that rate!

Lewis Carroll

Alice in Wonderland

There are several ways of writing down the equation that represents a traveling wave. Some are more precise than others, but you need to know a little mathematics to be able to understand them. On the principle that when you need to explain something you should use the simplest explanation that doesn’t involve cheating, we have chosen one that has nothing more complicated than cosines. If you have done a little trigonometry and can remember that

$\mathrm{cos}X\mathrm{cos}Y={\scriptscriptstyle \frac{1}{2}}\mathrm{cos}(X+Y)+{\scriptscriptstyle \frac{1}{2}}\mathrm{cos}(X-Y)$

that is all ...

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