I find nerd material quite interesting even when it’s over my head. LOL
My first assumption of noise production would be the piston. Assuming most of us have piston compressors. To get the frequency of the noise (piston cycles), take the motor speed, figure out the pulley ratio, do the math to get the compressor speed. Since the piston goes up and down in one revolution, divide the compressor speed by 2. Get the units in “events” per second. This is how many times the piston is going up or down essentially. This is the frequency.
Then, you put the frequency in this formula as the WH and solve for V0 which is the volume. Build your muffler with this volume. I suspect this may be the volume of the silencer boxes on the compressors. Something like this is how they ‘engineer’ the solution instead of completely guessing.
Explore Helmholtz Resonance: the core principle governing how air volume and openings control sound frequency.
engineerfix.com
en.wikipedia.org