>> The sound wave produced by a piano note is a simple sine wave.

> No, it's not. A piano note is a complicated stack of overtones (some of which are harmonic and some of which aren't) and transients. If it was just a sine wave, it would sound like a sine wave and not like a piano.

This is really such a fundamental* aspect of frequencies and sound, it should have been the starting point of the article. "Look how noisy and squiggly this wave is, but with FFT we can see that it really only consists of waves at multiples of the same frequency".

* no pun intended