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Sound attenuation can occur due to various phenomena. The most known are

  • Distance: For a point source the sound pressure decreases by 6dB with each doubling of the distance to the sound source.
  • Atmospheric absorption: Depending on the air pressure, humidity and tempreature sound attenutate increasingly faster if the frequency is higher.

However only accounting for those two attenuation types is probably not enough to simulate real world sound attenuation.

I suppose scattering with air molecules could also contribute to attenuation, but I did not find any clues or formula. Rayleigh or Mie Scattering is propably not applicable, since lightwaves have much shorter wavelengths than soundwaves.

Therefore my question is, what types of sound attenuation exist, if we suppose we are in open space and have direct line of sight between the audio source and listener, and what known mathematical models exist for them?

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  • $\begingroup$ When you have sound insulation (which often is the same fiberglass insulation for retaining heat), there is attenuation. I dunno what you would call it. $\endgroup$ Nov 13, 2023 at 17:51
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    $\begingroup$ I believe this question is better suited for the Physics SE where there is an “Acoustics” tag. You may find some info (unfortunately not much) in this answer, but I strongly suggest you ask in the Physics SE site. $\endgroup$
    – ZaellixA
    Nov 13, 2023 at 21:54
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    $\begingroup$ I’m voting to close this question because it is a better fit for the physics.SE. $\endgroup$
    – MBaz
    Nov 13, 2023 at 22:27
  • $\begingroup$ You're basically listing diffraction (spreading out forward with distance), absorption (turns to heat) and scattering (redirection away from forward). From that framework I don't see what else is possible. You've got forward, not forward and absorption to heat. There are lots of other phenomena but they're broadly going to involve those three things. Maybe frequency conversion if you consider that a loss? $\endgroup$ Nov 14, 2023 at 2:32
  • $\begingroup$ Thank you for the suggestion @ZaellixA. I was hoping to get an answer with more hands on expierence regarding audio attenuation here. The idea is to decompose the source audio into multiple frequency bands and play all the decomposed audio at the same time, adjusting the volume for each channel to approximate sound attenuation without operating in the frequency domain. But only accounting for distance and atmospheric absorption does sound like some attenuation is missing. $\endgroup$
    – MrRabbit
    Nov 18, 2023 at 20:44

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You already got the two main mechanism for a homogeneous free field:

  1. Propagation attenuation. However, this depends on the shape of the wave form: For a spherical wave the energy indeed with $1/r^2$, for a cylindrical wave it drops with $1/r$ and for a plane wave for a diffuse field it doesn't drop at all.
  2. Medium losses. For air that mostly affects high frequencies and depends a fare bit on the humidity.

However, true free fields don't occur outside of an anechoic chamber, so this is typically insufficient to model a real world situation. In the real world there are always boundaries which result in "impedance discontinuities" .

  1. At a boundary some sound energy is reflected (specular of diffuse) and some sound energy transmits into the new medium.
  2. The reflected sound changes the shape of the wave form (and with it the propagation attenuation) and it interferes with the impeding sound wave. The inference is not a loss mechanism but it sure changes the sound pressure that you can measure
  3. The transmitted sound will be attenuated by the loss factor of the new medium. Typically that's the end of it, but depending on the situation is may also exit the medium again at a different boundary.
  4. At the edge of a boundary, sound is diffracted. This has effects similar to the reflected sound.
  5. A more esoteric one: a boundary close to a sound source changes the radiation impedance of the sound source and make it more efficient. That's the opposite of attenuation.

While free field is relatively simple to model, any real world sound field poses a significant challenge. The sound field in the room that you are sitting in while reading this is just horribly complicated.

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  • $\begingroup$ Thank you for pointing towards specular and diffuse reflection. I suppose to calculate the sound pressure level of the wave after the reflection at the boundary one could use lambertian (diffuse) and phong (specular) reflectance as an approximation? $\endgroup$
    – MrRabbit
    Nov 18, 2023 at 20:55

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