But think about it this way: if you have a plate moving back and forth in a square wave pattern at the surface of a pool of water, would the waves on the water be square?
Waves in water are surface gravity waves, which air does not have. Because water is pretty incompressible, high pressure causes a water column to rise against gravity. The rate at which the column falls back down is obviously dictated by gravity. The faster the frequency, the more a pressure wave acts like a real pressure wave and less like a surface gravity wave. Since real pressure waves don't rely on gravity for transmission, they travel far faster, resulting in dispersion[1]. You can still have square waves as long as they are 10-100x slower (longer) than normal waves.
Since air pressure does not typically produce a height difference in the atmosphere, standard sounds in air are not subject to dispersion and act very differently from water. There is obviously still a limit to the rise/fall time of a square wave, when the transition is more like a shockwave front, but that's a very square wave.
No, but because surface waves behave differently from sound waves (which are in "3D") https://en.wikipedia.org/wiki/Dispersion_(water_waves) Basically phase velocity changes with the amplitude and the shallowness of the water.
Yes it's easy to think they behave the same, but they don't.
Instead of flawed thought experiments you could try a quick test for yourself: hold your speaker up to your microphone, play a square wave, record sound, and look at the waveform.
(below is the original 440Hz square wave; above is the recorded sound)
The recorded waveform looks nothing like the original, and it sounds very different too: the original is much harsher, although the pitch sounds exactly the same, as expected.
Might be my crappy microphone? Or maybe the sound is being filtered somewhere along the way?
That waveform looks pretty good imo. When I did it, I the signal was very weak so the signal to noise ratio was bad. There were low frequency impulses from me moving the headphones around and regular hums from other sources.
My best guess for the large attack showing up there is not effects from the microphone, DAC, amp, or anything but the actual speaker. Good audio measurements are hard to come by thanks to all the snake oil, but square wave measurements are common when there is data. The physical models of transducers aren’t trivial, but in a single broad stroke the answer is “physics” and “spring-mass-damper”.
The decay is expected, as the pressure around the microphone can only temporarily increase before the pressure wave disperses into the room. As an extreme example, if you turned an entire wall into a speaker and played a square wave, you would be able to make a much more square shaped waveform. There’s no replacement for displacement baby (see: subwoofers). If you want a more square waveform, try using a headphone pushed right up to the mic and going to a higher frequency (like 1 kHz).
Edit: If you want to skip the trip down the rabbit hole: I think the end-all for audio quality are sealed in-ear monitors (IEMs). Low group delay from short distance from transducer to eardrum, and sealed enclosure for good bass response (see: square shaped low frequency square waves).
Visualizing the spectrum of a square wave is so easy, it’s used to teach the concept of the frequency domain. Less square square wave? You likely peeled off some higher harmonics and added some phase noise.
The point of the experiment is to demonstrate that sound waves in air are not at all like water waves and sonic square waves do, in fact, exist.
The sine-ness of the water waves comes more from the mass and "elasticity" of the water, and not from the impulse driving it. If you put the same plate in air (or a speaker cone projecting a square wave) the mass and elasticity of the air permits much more "equare"-like pressure waves.
