the note A vibrates at 440 hz. This is what is called a fundamental frequency. Only a pure sinewave will have only a fundamental frequency. If you analyze sound in a frequency spectrum analyzer, you will see the fundamental freq as well as any harmonics and overtones created by the instrument recorded. The reason why pianos and guitars have different sound even while playing the same note is because the physical shape and size of the string as well as its method of being struck cause different harmonics and overtones thus producing a different sound even with the same fundamental frequency.
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