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I am trying to understand why when we play a note on a stringed instrument, not only it oscillates with it's fundamental frequency but also the multiples of that. For instance if you play a D on the lowest string on the cello, it causes the one octave higher D string vibrate also, as well as all other multiples of the fundamental frequency. The explanation I've heard is that ''the string oscillates with all multiples of the fundamental frequency''. It seems to me any vibrating string with fixed ends oscillates with a a fixed frequency. What is meant by this sentence exactly? Does it have something to do with Fourier series?

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