Perhaps I misconstrued the question you appeared to ask in your previous post by saying, "It is also important to know whether Sabine coefficients include air dampening in their effect or not. I'm not sure I've read a clear statement about that anywhere." I wholeheartedly agree that air dampening matters in modeling reverberation. What I attempted to explain was that in experimental measurements of absorption coefficients, air dampening is not much of a factor.
There are three primary ways to measure the Sabine coefficients for a material sample: the reverberation chamber method, the Kundt tube (or standing-wave) method, and the tone-burst method.
The oldest way (which is still in practice due to the advantage of measuring real-world absorption effects) is the reverberation chamber. First, the RT60 (the time it takes for the sound power to decay by 60 dB) of the empty chamber is measured for a given band, then compared with the RT60 of the chamber with a sample placed within it. The advantage of testing in such an environment is that the sample will absorb sound impinging on it from all angles, just as it would behave in a real room; however, the disadvantage is that the effects of many different variables such as air dampening can skew the results somewhat, making it a bit less scientific (since the whole purpose is to measure the direct effect the sample has on incident energy).
The standing-wave method is a second approach that eliminates many of these variables by placing the sample in one end of a Kundt tube (which is only a meter or so in length) and a loudspeaker in the other. A microphone, telescoping through the center of the speaker, can be variably adjusted to measure the intensity at each node thus allowing for a more accurate measurement in a far less complex system. The main drawback is that the data gathered by this test is only truly accurate for sound striking the material at perpendicular incidence.
The third method I know of is the tone-burst method. In this test, a loudspeaker is first mounted a specified distance from the microphone and either tone-bursts, sine chirps, or MLS signals are used to measure the intensity of sound at this distance; by using these types of signals, only the direct sound is measured and all reverberation in the surrounding room is rejected. Then, the speaker is mounted at an angle to the sample and the microphone is mounted at the opposing angle, with the net distance equal to that of the first test. A barrier is placed between the source and mic to prevent direct sound energy from interfering with the results - the idea is to only measure the sound as it strikes the sample. The benefit to this method is first that environmental factors such as air dampening and diffraction are negated, and second that the coefficient can be obtained for any angle of incidence (resulting in a polar plot of the specular reflection).
In either of the final two approaches mentioned here, air dampening effects are negligible due to the fact that there is only a maximum of a few meters distance for the sound to travel.
I was able to find out that the measurements taken are of sound power, not pressure. This means that the equation to convert a Sabine coefficient into decibel attenuation would be:
Again, a coefficient of 1 has no solution and any greater than one would appear to introduce new sound energy into the system (which is obviously a physical impossibility). If one were really motivated to try and emulate this effect, they could multiply the area by the highest coefficient (and build the surface to this dimension), and then scale the coefficients so that the highest would equal 0.999. The only drawback would be that the increase in area might conflict with creating accurate position and geometry within the emulated room.
Getting back to air dampening momentarily, I wondered about how the program calculates this effect on each ray. From all the resources I found, air dampening is dependent on the temperature, barometric pressure, and relative humidity in the environment. However, in determining its absorptive effects you would use the volume of air in the environment.
I am assuming (although I admittedly don't know much about the programming aspect of these things) that each ray in your simulation is attenuated by a dampening coefficient as it travels from the source to the mic. In other words, if a ray travels X meters before it reaches its destination, then it will have lost Y intensity on its way. My question is whether that model would be accurate and applicable to air dampening. Two rooms may have the same volume of air, but with different dimensions and shapes that may affect how far sound must travel before it reaches the mic, thus changing the dampening effect when it should remain the same.
The ray-tracing concept of estimating reverberation characteristics seems to be the predominant model and produces fairly realistic results, but I also know for the most part wave mechanics prevails for lower frequencies while the higher frequencies tend to propagate more like rays.
Of course, since air dampening only really affects high frequencies, maybe this is all moot.
My brain is full. May I be excused?
Air dampening is modelled quite easily in Impulse Modeler: a length of travel between reflections is considered only. This is mostly enough as you can adjust the overall 'response' on the graph: thus you can model any kind of air conditions (if they are isotropic/linear - no wind, no falling rain).
The modeling using rays is fairly accurate in my opinion even for the lowest frequencies. Of course, Impulse Modeler can't be used for architectural modeling due to 2D space, but the overall model is valid, and even includes diffusion for modeling rough surfaces with broadband diffusion characteristics. For even better modeling each ray could carry a narrow-band spectral information: in this case each material could feature a frequency-dependent diffusion constant.
Of course, this model is unable to design non-linear spaces, so it is hardly usable for speaker cabinet modeling.
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