Estimating Sound Absorption Coefficient (RT60 Technique)

[Aural-Aid]

Hi friends of SOFT!

I would like to share something with the clever community here and find out what they think. Sometime ago, I was playing around with Sabine's equation and found out that you could estimate sound absorption coefficients using RT60 instead of the ASTM C423's method of using decay rate (dB/S).

Here are the workings (I do apologise for not using mathematical symbols as the thread does not display them properly)

Let's start with Sabine's Formula (RT60)

RT60 = 4ln10^6/c * V/A = (approx) 0.1611V/A ---(1)

where

A = Summation aiSi
ai = absorption coefficient of i
Si = surface area of i
V = is the volume of the room in m³​

In a reverberation chamber with materials to be tested,

A = Summation aiSi = arSr + amSm

where

r = of reverberation chamber (e.g. Sr = surface area of reverberation chamber in m²)
m = of material tested (e.g. am = absorption coefficient of material tested)​

Therefore, RT60 = 0.1611V/(arSr + amSm)

Finding am,

am = (0.1611V/RT60Sm) - (arSr/Sm) ---(2)​

Since the surfaces of a reverberation chamber are almost perfectly reflective, ar = u where u is a very small number.

Therefore am can be approximated to

am = (approx) 0.1611V/RT60Sm​

How does this method reconcile with ASTM C423's method?

ASTM C423-09a uses Sabine's equation (decay rate dB/s)

A = 0.9210 Vd/c ---(3)​

to derive

a = (A2 - A1)/Sm ---(4)

where
A2 = Absorption (Sabines) of reverberation chamber with materials
A1 = Absorption (Sabines) of reverberation chamber without materials
Sm = Surface area of material​

Since equation (1) and (3) are just different sides of the same equation where 0.9210d = 4ln10^6/RT60, we will focus on reconciling equation (2) and (4).

From (1)

A = 0.1611V/RT60 = Summation aiSi​

Looking at (4)

A1 = arSr
A2 = 0.1611V/RT60​

Since am = (A2 - A1)/Sm ---(4)

am = [(0.1611V/RT60) - (arSr)]/Sm
am = (0.1611V/RT60Sm) - (arSr/Sm)​

where (arSr/Sm) is a small number since ar is negligible.

am = (approx) 0.1611V/RT60Sm​

Therefore equation (2) and (4) are reconciled.​

TL;DR - Using RT60, you could estimate the sound absorption coefficient of your materials with this formula

am = (approx) 0.1611V/RT60Sm

where

am = absorption coefficient of material tested
V = is the volume of the reflective room in m³
Sm = Surface area of material tested in m²​

Note: For an accurate measure, the size of the room needs to be about 200 m³.​

Thanks for reading this far and may you have a great weekend ahead!