Why sine wave is the natural wave, why not something else?
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It’s the simplest geometrical (or mechanical) situation: something rotating around an axis (a fixed point) will have a sine (or cosine) movement when projected onto a line.
If you leave aside the movement, sine and cosine are unavoidable each time you have a projection: your shadow on the ground, mapmaking, video game rendering, &c.
On the other hand if things change/move, you can mathematically represent nearly any situation by combining various sines and cosines (so-called Fourier decomposition). It just so happens that sines and cosines have awfully pleasant mathematical properties. A piano note for example can easily by analyzed into a superposition of sine (and cosine) vibrations.
That being said, there are other methods/waves, e. g. [wavelets](https://en.wikipedia.org/wiki/Wavelet).
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