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

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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

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”.

Air doesn’t “know” frequencies. Frequencies are how we analyze vibrations. It is a human construct – air simply changes in pressure from point to point and that pressure is transmitted. For our human interpretation both in the experience of listening and for technical analysis, we break it down into different frequencies, loudness etc.

How we distinguish a violin from a cymbal is due to our brains. Everything about how we perceive our environment is constructed by our brains.

For example, sugar doesn’t “know” it is sweet. When we mix ingredients to cook food, the food doesn’t know what it tastes like. Our brains break it down (due to the way our organs work) into concepts of sweet, salty etc and finally make a decision (based on a learned response) whether “this is beef steak” or “this is chicken soup”.

Let’s simplify the question and ignore the notions of timbre, harmonics and fundamental frequencies to avoid technical words.
If we just ask, how can we hear 2 notes at the same time with just one air it becomes very simple to illustrate.
A note is just how many times per second the air is moving next to your ear, making your eardrum move at the same rate. The faster, the higher the pitch and vice versa.
Now imagine that you are holding a rope and you wiggle your arm up and down say twice per second. It will create this wave pattern all along the rope (if you can’t visualise it just try it!). This is one note (2 time per second note).
Now if you were to jump up and down once every second while still wiggling your arm twice per second you will keep the small wiggle in the rope, but your jumping will add a bigger wiggle every second time and create a different pattern (where every second swing in the rope a twice as big).
You can imagine an infinite combination of wiggles that creates different wave shapes along the rope. Your brain learns along your life that these patterns come from such and such noises and makes out the “sound meaning” for you.

So waves (including sound waves) are pretty complicated and pretty cool.

First thing to mention: resonant frequencies. Have you ever been walking with a cup of water, and even though you’re not walking super fast, the water just starts sloshing really bad and spills out? That’s because your walking speed happened to hit the resonant frequency of the water.

Some things like to vibrate at certain frequencies. Imagine pushing a kid on a swing. If you push at random times, that kid isn’t going anywhere. But if you push at just the right time, in the right rhythm, that kid swings higher and higher, right? When you slosh the water, you accidentally walked at just the right speed and “pushed the kid on the swing” at just the right time, making the water slosh higher and higher.

So that’s the first part. Next thing is waves.

That kid on a swing basically represents the simplest kind of wave. They go up and down at an even, constant rhythm. Up, down, up, down, always the same time (in a perfect, hypothetical world, for the sake of this example).

The cool thing about simple waves is, they add together to make complicated waves. So you take a wave at 4 Hz (that’s 4 up and downs per second) and add it to a 3 Hz wave and a 5 Hz wave and you get an even more complicated wave.

And the coolest thing is, you can take that complicated wave and separate it back out into the simple waves! That works by the resonant frequencies mentioned above. Imagine you were pushing the kid on a swing with some complicated pattern, but among the seemingly random pushes, some of the pushes are just the right timing to make the kid swing higher. Even though your push pattern is super complicated, when we see the kid starts swinging higher, we know that somewhere in that pattern is the perfect swing frequency.

Your ear contains tons of swings of different sizes that respond to different rhythms (frequencies). A sound wave (that complicated swing pushing pattern) passes through all those swings, and *some* of them start swinging. So your brain knows that in that super complicated pattern, there was actually *this* frequency and *that* frequency.

And your brain has a big database of different frequency patterns and what those mean. So that’s why you can hear violins and trombones and drums in just the vibration of air.

As far as my brain simplifies this, it goes like this:

Yes it is just one air vibrating. But if you can apply a filter on it, you can divide this vibration into simpler vibrations.

Kinda like how a prism can filter out the sunlight into various colors, the cochlea inside your ear can filter out the various simple vibrations from the complex vibrations hitting your ear.

There are tiny hairs inside the cochlea, each vibrates at a different frequency. So when the complex vibrations from the air hit your ear, only very specific hairs will vibrate giving you the sensation that you can hear the drums and violins.

Another way to look at it is when you throw a rock in a puddle, it creates ripples. If you throw more rocks, by your logic water should only carry ripples from one of them, but instead these ripples merge/mix. If you stand far enough from the point where you threw the rocks, you will indeed see just one ripple, but if you apply a filter on these ripples you will be able to see that this apparently one ripple is complex and causes by throwing more than just one rock. Kinda like how your brain knows that despite only listening to just one complex vibration in the air, you can actually hear many different frequencies at the same time