So there's this thing called a Fourier series...

Basically any wave can be created by adding together individual frequencies, and with some fancy math it's possible to go the other way with a Fourier transform and get how loud every frequency is (like is displayed in a spectrogram).

I think the real black magic is in how our ears and brains can decode the mess of information coming in and identify meaningful patterns.

That's because it doesn't, your brain does

Speakers do the simplest thing possible and literally just vibrate. A recording being played literally just recreates a recorded vibration. It's a tiny choreography that your ears are incredibly sensitive for.

All the fancy stuff happens in our brains, after our ears has split up the sound around us into different ranges of frequencies (you can think of the hairs in the inner ears as tuning forks). We learn to recognize which frequencies goes together, and then we learn how the frequencies from multiple sources can overlap, and we learn what it all means

The real crazy part is how something as simple as sound can carry so much information and how reliably our brains can tell it all apart and make sense of it

How speakers work in general is just black magic to me, actually.

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An easier way to understand it, without knowing the math, is to know how it's made. You play audio into a very similar device and it's needle scratches the grooves. When you then have a needle pick up the grooves it's moving the exact same way the needle was forced to move by the original.

It's similar to how a speaker and a microphone are basically the same device. If you take a speaker and plug it into a microphone input, it still works (though they're tuned differently so it's not as good). A microphone has a crystal vibrate, which creates an electric signal. If you play that electric signal into a crystal it vibrates and creates the same sound.

There's no math or anything being done for this to work. It's purely mechanical. It's just a copy of what the needle did when sound was played into it, so another needle running through it recreates the same sound. You can use math to represent it, but none is being done by the device (other than just the laws of physics).

Here's a video on the topic.

This is from a video about headphones. His layman's explanation at the timestamp is probably the best I've heard it told:

https://youtu.be/4-rgrSFrwrs?t=647