| > The beginner question is, why don't we use triangle waves of square waves You can think in terms of complex exponentials, and the use of complex numbers makes even more sense when you know the differential equations can be solved by polynomial methods, which naturally leads to complex numbers. However you can also answer "why sine waves not triangle/square waves" with a geometrical answer. (This is how I learned it at school, before I knew about complex numbers or differential equations.) A property of sine waves is that their sums and products are also sine waves or simple combinations of a small number of sine waves. The sine wave shape persists. This neat property is unique to sine waves, and you can think of it as a type of symmetry. For example, in the simplest cases: adding two sine waves with the same frequency and different phase produces another sine wave with that same frequency. Multiplying two sine waves with different frequencies produces the same as a sum of two sine waves, having the sum-of-frequencies and difference-of-frequencies. Doing so with any other wave shape results in a different wave shape than you started with. A lot of audio and radio signal processing depends on this property, and the way sum-of-frequencies and difference-of-frequencies works for every sine wave component at the same time. Our whole concept of a radio "band" of signals that you can tune into comes from it. |