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I want to put acoustic panels in a space to help reduce reverberation (RT60 is a measurement of how long it takes sound to decay by 60 dB). I have already calculated how many panels should theoretically be needed, but I decided to perform an experiment.

I had a number of panels on hand and set them up temporarily around the room and took periodic measurements as I set them up. I did not have enough panels to lower the reverberation to my final goal but I was hoping to use the measurements to create a trendline that I could use to extrapolate to predict how many panels it would take to achieve my desired goal.

Here is my actual measured data:

Sq Ft Panels    RT60
------------    ----
  0             3.07
 48             2.84
 96             2.65
192             2.43
288             2.21
336             2.16
480             2.02

and here is a graph of this data: Graph

So, how do I determine what kind of function likely represents this data so I can then predict what a larger value for the Sq Ft Panels (like 1000) would yield for RT60?

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  • $\begingroup$ The good statistical textbook will tell you that extrapolation is not good practice. $\endgroup$
    – user158565
    Commented Jun 4, 2019 at 2:11
  • $\begingroup$ Welcome to CV! The amount of sound suppression is most likely subject to not only the proportion of coverage of the walls, but also the placement of the panels. Square feet of panels is a bit strange a measure, as the amount clearly depends on the size of the room. $\endgroup$
    – Frans Rodenburg
    Commented Jun 4, 2019 at 5:54
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    $\begingroup$ That said, for this particular room, using these particular panels, and after trying various configurations with the same amount of square feet of panel, you can probably get a reasonable idea with an exponential fit. Of course, this is just a crude approximation, as any new panels will have different placement and configuration options and more importantly, your room probably has finite square feet of wall to cover. $\endgroup$
    – Frans Rodenburg
    Commented Jun 4, 2019 at 6:00
  • $\begingroup$ Thanks! Yes, the amount definitely depends on the size of the room! Perhaps I did not make it clear but these numbers aren't just theoretical but are measured in an existing gym that I'm volunteering for. So I can't change the size of the room, just what's on the walls! Reverberation depends both on the room volume as well as the absorption coefficients of the surfaces. By adding "wall panels" I am changing the absorption coefficients of the surface area they cover to reduce reverberation, so that's why I'm using Sq Ft Panels as my variable, as room volume is fixed and absorption is constant $\endgroup$
    – Nick
    Commented Jun 5, 2019 at 13:40
  • $\begingroup$ And it might not seem intuitive but for a large space (like a gym), placement of absorbing materials doesn't matter too much as sound is bouncing off walls somewhere around 80 times before decaying by 60 dB, so no matter where the panels are placed the sound waves will end up hitting the panels. Typical coverage for sound panels is around 15%-20% of wall surface area. If anyone wants to know more about sound absorption they can look up the Sabine Equation. But for purpose of my question that is probably more information than necessary. $\endgroup$
    – Nick
    Commented Jun 5, 2019 at 13:43

1 Answer 1

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I performed an equation search on your posted data, and a simple logistic type equation "RT60 = a / (1.0 + b * exp(-1.0 * c * SqFt))" gave a good fit with R-squared = 0.9986 and RMSE = 0.01321 for parameters a = 1.7057854638508458E+00, b = -4.4410554473409003E-01, and c = 2.2134460779528603E-03

plot

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    $\begingroup$ @FransRodenburg as an aside, I lived in Tokyo's Azabu-Juban district in the late 1990's. $\endgroup$
    – James Phillips
    Commented Jun 4, 2019 at 12:27
  • $\begingroup$ Thanks James! This was just what I was looking at doing. Do you have any links to how one would do this "equation search" to find the equation you used, and also how the parameters were found? I'd like to try this with some related data to see if I can do it. $\endgroup$
    – Nick
    Commented Jun 5, 2019 at 13:45
  • $\begingroup$ @Nick I used the "Function Finder" on my zunzun.com Python open source curve and surface fitting web site to run the data through a couple of hundred known, named equations. For non-linear equations it uses the Differential Evolution genetic algorithm to determine initial parameter estimates for the non-linear solver. The direct link is zunzun.com/FunctionFinder__W___/2 and it has test data, after looking at the different options just hit the "Submit" button to give it a try. $\endgroup$
    – James Phillips
    Commented Jun 5, 2019 at 14:14

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