What types of sound attenuation do exist?

Question

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?

Answer 1

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.