Is the total attenuation of a material at a specific frequency the sum of the sustain value and the damping value for that frequency? i.e. if the 'Sustain' value is set to -2.0 decibels and the 'Damping Value' at 9,000 Hertz is -1.0 DB, is the total 'Damping' at 9,000 Herz -3.0 DB? Is 'Sustain' simply a 'Global' value for ease of use? Is the damping value in decibels? How do Sabine absorbtion coefficients relate to decibels, i.e. if window glass has an absorbtion coifficient of .31 at 150 Hertz, what values would you set for 'Sustain' and 'Damping'?
I am hoping to create a detailed list of 'Materials' for modelling with realistic absorbtion characteristics based on published coefficients of absorbtion.
Yes, 'Sustain' is a global value for ease of use - in your example damping at 9kHz will be exactly -3 dB/reflection.
There should be a way to translate Sabine coeffs into Impulse Modeler form, but I have no clue how to do it. Moreover, when I was designing Impulse Modeler I've chosen frequency points which are not compatible with ISO Sabine measurements. So, this can also pose a problem.
Thanks for the clarification. I am not a sound expert, byt if you refer to Loudness Chart it gives a correlation between sound level changes in decibels to acoustic energy loss (absorbtion coefficient??). The formula for this is 20 log ((1/(1- C))^.5)). This appears to look alright but it should be confirmed by someone with more physics background than me!!
So, I would suggest that for future enhancements you consider using the standard frequency octaves for sound absorbtion data as well as giving the user the option to enter values as coefficents. The user could then design rooms modelled after real life rooms and hopefully better estimate the reverberation from that room. Possibly this software could be used by acoustics designers to predict the acoustics of a room in future software generations.
I developed the formula intuitively (and therfore it may not be correct!!) based upon the following facts and assumptions:
As sound radiates out from a source it's energy level reduces according to the inverse square law. i.e. if you double your distance form the source the energy level will be 1/4, if you are 4 times the distance the energy level will be 1/16.
Doubling the distance form a source will result in a decrease in sound level of 6 dB (ignoring the loss due to absorbtion by air). This can be expressed in a formula: dB(loss) = 20 log(range), where range is the increase in the distance form the source. (2 = twice the distance, 4 = four times the distance, etc.) So, double the distance and get a loss of 20 log (2)dB = 6.02dB, four times the distance and the loss is 20log(4) = 12.04bB, etc.
Attenuating the energy of a sound source by .5 will result in a reduction of the sound level by 6 dB. If you reduce it by .75 (to a level of .25) it will result in a reduction of 12dB.
It appeared to me that you could reduce a sound's energy level by either moving away from it, or staying in a fixed location and attenuating it (absorbing it?) and that the relationship was similar in that doubling your distance reduced the sound level to .25 (absorbtion coefficient), and that both resulted in a 6dB reduction which could be expressed by the formula 20log(x) where 'x' is the range if you are moving away from the source, and 'x' = the square root of (1/(1-c)), where c represents the Sabine absorbtion coefficient.
The final formula then is:
reduction in sound loss (dB) = 20log((1/(1-c))^.5) where c = absorbtion coefficicent
This should be verified by someone with more phsics backgound than me.
I guess your points 1 and 2 may not be correct. Where have you found such laws?
On your point 3, I'm not sure this relates to Sabine coefficients. Of course, when converting multiplier 0.5 to log scale (decibells) you'll get -6 dB. But does this really has something to do with Sabines?
I found most of these references on the internet. I also have a copy of "The Master Handbook of Acoustics", 3rd Edition by F. Alton Everest, published by McGraw Hill. It states in chapter 4, "Intensity of sound is inversely proportional to the square of the distance in a free field." It also states that "..sound pressure level is reduced 6 dB for each doubling of space.".
Refer to http://www.lenardaudio.com/education/04_acoustics.html. This web page about 2/3 down the page under the subheadings "(2) Absorbing Sound" and "(3) Understanding dB For Sound Absorption" use absorption coefficient and % sound energy absorption interchangeably. It also demonstrates the following absorption coefficients result in the following dB reduction:
.5 results in -3 dB
.9 results in -10 dB
If you use the formula: reduction in sound loss (dB) = 20log((1/(1-c))^.5) where c = absorption coefficient
You get the same results.
Now I think I'm over my head!
OK, I understand.
Since 'air dampening' is exponential in its nature, then of course, the rule 1 may be correct. However, it does not state the 'medium coefficient', because air in different conditions has different absorption coefficients so that at the given distance sound is attenuated differently in different air conditions.
Moreover, it seems that rule 1 and 2 are interchangable.
I think your formula needs more research for sure. Since it gives a discrete 'dampening' paramter in decibells it should be proved that it provides the correct result if applied to an infinite number of rays bouncing off the surface described by the given Sabine coefficients.
In general, such formula could be very useful, because the ray tracing algorithm that is used for such modeling in most cases (not only in Impulse Modeler case) relies on discrete dampening coefficients.
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 know these are old posts, but during a random late-night search I stumbled upon this rather interesting thread.
This shouldn't be too hard to approximate with a fairly straight-forward equation, but there are some things to consider.
First, a specified Sabine absorption coefficient is a measure of the efficiency of absorption. Therefore, if a given material absorbs 50% of the incident energy, then the Sabine coefficient is 0.5; if the material is acoustically "black" (meaning it absorbs 100% of the incident energy), then the coefficient is 1. One problem (to which I am trying to find the answer) is whether this is calculated in laboratory testing as a loss of acoustic pressure or a loss of acoustic power, since this will change the rules for setting up a proper equation.
The equation shouldn't really be too difficult, since the absorption coefficient is basically (reflected energy)/(incident energy). Since decibels are simply a ratio of a given energy to a reference level, the Sabine coefficient should crank in rather nicely. However, the equation above has no solution for a coefficient of 1 (which in a way makes sense - a perfect absorber would have infinite attenuation).
Another problem is that it is common in testing for materials to register coefficients above 1. Obviously, an object can't absorb more than 100% of the energy imparted to it, but the reason for this is due to diffraction of a sound from the edges of the material sample. I'm not certain how this would be replicated, other than to assume 1 as a ceiling value (which is common practice in many cases).
To answer your question the effect of air dampening should be negligible from what I understand. Anything I've read of the testing procedures indicates that the two ways Sabine coefficients are experimentally obtained are by either using a Kundt tube or by measuring tone bursts with two microphones (one measures the direct sound, another measures the reflected sound at an equal distance from the source) and gates screen out reverberant reflections from other surfaces. In either case, the distance from the sound source to the transducer is so small (no more than a meter or so) that the direct sound being measured shouldn't suffer from any effect from the air.
I hope this helps, although I wonder if this conversation might have expired after three years. I'll check back anyhow, and if I find something I'll post it.
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