Speed of sound should be constant

[alexcjohnson]

Love the tutorial! But one thing bothers me - the air molecule grid shows one period across its width, independent of frequency, which implies that the speed of sound is linearly proportional to frequency.

Constant speed as a function of frequency is much closer to the behavior of air, which would require the number of periods visible across the width to be linearly proportional to frequency.

[joshwcomeau]

Ah, interesting! This wasn't at all on my radar.

I looked into fixing this, but I'm feeling a bit confused by this...

I updated it so that the number of periods visible was equal to the frequency (so, 2 periods for a frequency of 2Hz). I get a GIF that looks rather unpleasant:

The issue is that the particles themselves vibrate at the speed specified; with these two things combined, the animation is too fast to make sense.

It's unclear to me how to reconcile this... Suggestions welcome, although truthfully I don't anticipate having that much time to work on this :/

[alexcjohnson]

Right - at higher frequencies the air molecules in your simulation start to overlap each other, since there's a bigger phase difference between successive lines. This opens up all sorts of interesting observations, which is partly why I brought it up. The loudness of sound is more closely related to pressure than to displacement, and pressure is proportional to displacement * frequency. This is actually there in the visualization as well: pressure is basically how far apart the molecules are from each other, so when your molecules start to overlap each other, that indicates a very high pressure!

So if your goal is to visualize equally loud sounds at different frequencies, I would suggest to also make the displacement scale inversely with frequency. I suspect that this would also keep the animation looking good, as it would keep the molecules from overlapping. Then perhaps add a little bit to the "Amplitude = loudness" is a bit of an oversimplification note - or a new note near the molecules visualizations - about displacement vs pressure and how this is also why you can see woofers move but not tweeters - the displacements are so much more at low frequencies.