The note you hear is the fundamental frequency of the sound wave. This is the main way that instrument causes vibrations. But there are many ways for a string, drum membrane, or tube of air to vibrate.
Since instruments use different materials and are crafted differently, each and every instrument will activate these other vibrations – called harmonics – at different levels of intensity. Musicians refer to this expression of harmonics as timbre, while physicists refer to them as the sound’s frequency spectrum.
I suggest you download a FFT Spectrum Analyzer app on your phone and repeatedly play a single note for it. Perhaps try whistling loudly. You’ll notice a VERY large peak (the fundamental frequency) and a bunch of tinier peaks (the harmonics).
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