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I dont know a lot about how sound waves work, so this question might sound stupid, but as far as I know the frequency determines the pitch and the amplitude determines the volume.

What confuses me is how unpitched instruments work, because all waves should have a frequency, and thus a pitch.

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all waves should have a frequency, and thus a pitch

No. In order to define a frequency of the wave, there must be periodicity.

The simplest to describe pitched sound is a sine wave – it keeps repeating over and over. Most instruments generate waves that can be described as a sum of several (or several tens) of sine waves, with some fundamental frequency f, the next twice higher: 2f, another tripled: 3f and so on. The wave formed by the sum of them repeats with frequency f. (Sometimes some frequencies in this sequence are missing or are not heard, but the sum of them still repeats with frequency f).

Waves of unpitched sounds cannot be described by a sum of limited (small) number of sine waves with frequencies being multiples of a common fundamental. We can still mathematically try to answer the question: sum of what sine waves would form this wave?, but the answer is: infinite number of sine waves covering a continuous range of frequencies. Such waveform doesn't repeat.

In practice the distinction isn't binary. Most pitched instruments produce some unpitched sounds with continuous spectrum, like the sound of piano hammer hitting the string or hiss of air in a wind instrument. On the other hand while unpitched instruments produce a continuous range of frequencies, they may emphasize some subrange of it strongly enough that a pitch can be recognized; this way, generally considered unpitched drums still can be tuned to a given note.

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    The middle paragraph could be a bit more accurate. It is possible to combine a finite number of sine waves in the audio spectrum and produce an unpitched sound. All that is required is that the sine waves used do not have a harmonic relationship to each other and also span a wide enough bandwidth. Sep 10 at 20:34
  • Todd is right - "Waves of unpitched sounds cannot be described by a sum of limited number of sine waves" is definitely untrue. Did you mean "Waves of unpitched sounds cannot be described by a sum of limited number of sine waves whose frequencies are multiples of a common fundamental"? (Even if so, there are many sounds that we'd describe as pitched that don't only have components whose frequencies are multiples of a common fundamental).
    – topo morto
    Sep 10 at 20:44
  • @ToddWilcox you're right, but this also opens a Pandora box of variety of musical instruments and pitch perception. I know I'm oversimplifying a bit, but I don't know how to do it better. I want to focus on the edge cases, as there is no simple boundary where a sound is no longer pitched. I'd just like to stress when I write "limited" I mean more "small" than "finite", since "finite" can be large. Yes, you can approximate a continuous spectrum with a large number of sine waves. Sep 10 at 21:06

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