I've just been working on making an abstraction for the inverse square law to control the volume of an audio source based on distance. The maths seems okay.

https://www.engineeringtoolbox.com/inverse-square-law-d_890.html

The mystery I can't figure out is that when the distance between distance 1 and distance 2 is 0, there's a discrepancy in volume, which should not be there (see screenshot).

Edit: I said 'should be there' when I meant 'should not'!

I'm also attaching the patches. I'm a bit perplexed, but it could be something very simple that I'm not accounting for!

test-inverse_sq_law.pd
inverse_sq_law.pd

You can see in the screenshot that the noise signal at input is indeed around -5dB as you say. But at the output stage, it's lower by a few dB. This is despite the rms value after the inverse_sq_law abstraction being the same as that going into the abstraction. That's what's stumping me.

BUT: That's much too complicated! You don't even have to analyze the signal with [env~]. Under the link that you posted there's a table from which you can see, that doubling the distance corresponds to a decrease of sound pressure by 6dB, which is 1/4 power or 1/2 amplitude. So I guess all you have to do is to multiply the signal with d1/d2.

If you're not making the assumption I think you are, then why are you computing the difference between the log math and the output of [env~] in [inverse_sq_law]?

Why is it not enough to just divide distance 1 by distance 2 (both non-zero) and take that as your RMS factor? e.g.

Edit: I cross posted with @manuels ... didn't intend to repeat what he wrote

I suppose I was trying to exactly replicate the inverse square law equation at the link in my first post so that I could that I check that I was doing everything correctly. When I checked my abstraction against the examples on the site, I seemed to be getting the correct outputs. What stumped me was why this wasn't translating when applying the abstraction's output to the [*~] in the patch with a sound source. I definitely made an assumption here that I wasn't expecting @jameslo.

@manuels I understand that it might not strictly be necessary and thank you for pointing out that you can just multiply the signal by d1/d2 divided. I will definitely do that for actual calculations!

@jameslo I wonder if you're being pedantic about my phrasing, which is fine. I do understand that division by 0 would be 0. That is totally fine in this situation, where I was do that as part of a formula to calculate the reduction in dB at distance 2, and then subtracting that from the dB of the sound at a hypothetical distance 1 (even if it's a bit unnecessary). As I said, I was following the equation at the link to check my work.