So yes, an (uncompressed) audio stream is just a sequence of samples of pressure (or displacement, depending on the medium).
The variety you get comes from the high sampling frequency: a high sampling frequency allows representing vibrations of the air pressure at many frequencies.
Yes.
> I had always assumed you needed to record different wavelengths of sound to capture different pitches
Why? Look at a mono vinyl record. It has a single groove, which is the soundwave carved into the vinyl. Digital audio is the same, except you store a digital image of the groove.
>Is my mental model completely wrong?
Yes.
>How do you get such variety in sound just from recording the volume?
By recording the volume 44100 times per second.
Samples of pressure (or displacement, minor phase difference), so kinda yeah.
How one gets so much variety? By sampling it really often. If you sample it 40000 times per second you actually get the full information for all pitches that are between 0 and 20000Hz.
If you don’t sample it often enough you don’t get all the information needed to store the sound. So yes we kinda indirectly do capture all the different pitches.
The magic is the linearity of the signals. They are additive. The different signals pass through the same stream of samples without interacting.
If you add volumes from sine wave in 400 Hz to sine wave in 300 Hz, you can transfer them together in a stream of samples , then separate them later.
Mathematically: f(at + bt) = af(t) + bf(t)
So different wavelengths added together will tell your brain there are different pitches at the same time.
When all those different wavelengths are using the same volume at the same time you can imagine that all those added waves will become a mess. That is what is called noise.
But when a high pitch wave is 'traveling' on top of a low pitch wave your brain can distinguish the different pitches.
What reaches your ears is continuous differences in the air pressure. That's more-or-less a single changing 'amplitude'. From that, your brain can pull apart the fundamental and overtone pitches from each source ... and sort them out so you can identify each one. Amazing technology ... almost indistinguishable from magic!
These days lots of people haven't seen audio on an oscilloscope ... which shows changes in amplitude with time. Look at this video. You'll see that at each point in time (left to right), there's ONE amplitude, whether he plays one string or more.
Both exist and are beeing used, but Samples are the default in uncompressed audio.
https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampli...
Depends on what you mean by 'record'. Generally the air pressure is sampled instantaneously, but it can be broken down into frequency components before recording/perceiving. That's kind of how our ears work and in DSP you do an FFT (which you can then pass through an iFFT to synthesize the original signal).