system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: How do we distinguish the sound from two different instruments playing the same tune when they produce the same frequency?

On a physical level, what's the difference between sound waves from two different sound sources that produce sound of the same frequency? Do the sound waves from a piano have some inherent difference to those of a violin or a trumpet?
gpt
Basically, the frequency we assign each note on an instrument is only the main, or loudest, frequency that's being produced. If you listen to a sine wave, what you're hearing is just a particular frequency and nothing else. When you listen to something like a piano or a violin, you're hearing that particular frequency, but also a lot of other, quieter, frequencies that give the note a different "timbre", or audible identity. These frequencies are always mathematically related(3/2 the base frequency, or so on) and depend on the particular construction and material of the instrument or sound source. These other frequencies are what give instruments different identities from each other, and are why you can't just replace a piano with a guitar or something similar. If you want to look into it in more depth and technicality, I'd suggest the wikipedia page for timbre.