So if an A is 440hz, why does a piano playing an A sound different than a violin, a guitar, or someone’s voice making that same A 440 note? It’s obvious that the pitch is the same on each instrument but each instrument has a distinct sound. I’ve never heard an A on a piano and thought, is that a piano or a cello. Why can we distinguish between instruments?
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No instrument plays a pure sine wave tone. The note you hear is the fundamental, e.g. 440 Hz, but there can be dozens of over/undertones mixed in. This is the timbre others have mentioned, exactly what an instrument sounds like that distinguishes it from all others. Look up polyphonic or overtone singing by Anna Maria Hefele on YT for a great intro and demo on overtones.
Those additional frequencies will interact with each other either constructively or destructively, depending on their strength and the instrument played, creating additional harmonics and beats that wouldn’t normally be there when the instruments are played alone.
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