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That is because of linearity/superposition - look up both of those concepts for more info. Basically, you can add as many sounds together as you'd like and it is the same as a single, different sound - so if you can recreate the one sound, you can recreate all of them.
The speaker doesn't know "this part of the wave is from the drum and that part is from the guitar", etc
Which is still mind blowing in its own right. What's incredible in the end is not so much the process of sound recording as the nature of reality itself.
For this part of the equation I find it useful to think of two tin cans with a string between them, which is a perfectly capable microphone/loudspeaker set-up.
Which in turn makes sound isolation even more mind-blowing!
So is that information deduced by the listener's mind, as opposed to their ear? Kind of like depth perception in the field of vision?
In short, yes.
Ear as an organ is not a simple microphone though. It’s partially evolved in a way to help humans recognize ‘the music’ and ‘the speech’. The brain does the heavy lifting.