How do we hear multiple sounds when it’s just one air vibrating?

Question

Like for example when I’m listening to an orchestra I can hear a clarinet and a violin quite distinctly from one another, but they’re both sounds vibrating through the same air. Logically, shouldn’t one air only be able to carry one frequency (Vibrate in only one way)? How does the air contain so many frequencies simultaneously?

In: 80

Answer 1

firstly, you think of a violin playing a single note as a single vibration, but it isn’t.

have you ever wondered how come you can even tell a Middle C played by a violin from a middle C played by a clarinet?

instruments (as well as human voice) don’t just produce a single note. they produce base note plus a range of harmonic frequencies that changes the “flavor” of the baseline note. every instrument has a different harmonic profile, so they sound different even if they’re playing same base note. so really even just a single violin playing a single note is ALREADY a series of overlapping “pure” notes.

so how is it physically possible to have multiple vibrations at the same time? it’s enabled by the superposition property of waves. you can take two different waves, add them up, and create a single wave that is a combination of the original two ([here’s an example of how that looks](https://www.acs.psu.edu/drussell/Demos/superposition/beats.gif)). the important thing is that you didn’t lose any information by doing this, so if you have the correct mathematical tool, you can take that complex wave, and separate it out to its fundamental frequencies.

now our brain can’t really separate out the fundamental frequencies inside each note like we could mathematically, but what it CAN do quite easily with some experience is separate out two notes (each of which is a series of frequencies). that’s why you can hear a piano and a violin and hear it as “piano+violin” instead of some alien middle sound.

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in the same vein, it’s also how we can tell a chord from a single note.

our brain can tell that the incoming signal is separable to multiple different notes, so that’s how we perceive it.

you could use mathematical analysis to further break each of those notes down to their harmonics and build a mathematically accurate profile of the chord, but our brain can’t go that far, which is why we still perceive of notes as “single”.