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Old 19th September 2019
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Originally Posted by Soundman2020 View Post

Here's the full set of equations for roughly estimating the isolation in each of the three frequency ranges:

First, you have to think of the wall as being a pair of single leaf barriers, so you need Mass Law equation again:

TL = 14.5 log (M * 0.205) + 23 dB

Where: M = Surface density in kg/m2

Now you need to calculate the above for EACH leaf separately (call the results "R1" and "R2").

Next, you need to forget that it is a pair of single leaf walls, and start thinking of it as a resonant two-leaf wall, so you need to know the resonant frequency of that system, using the MSM resonance equation:

f0 = C [ (m1 + m2) / (m1 x m2 x d)]^0.5

C=constant (60 if the cavity is empty, 43 if you fill it with suitable insulation)
m1=mass of first leaf (kg/m^2 or lbs/ft2)
m2 mass of second leaf (kg/m^2 or lbs/ft2)
d=depth of cavity (m or ft)

(C=43 for imperial empty, 1897 for metric)

Then you use the following three equations to determine the isolation that your wall will provide for each of the three frequency ranges:

R = 20log(f * (m1 + m2) ) - 47 ...[for the region where f < f0]
R = (R1 + R2)/2 + 20log(f * d) - 29 ...[for the region where f0 < f < f1]
R = R1 + R2 + 6 ...[for the region where f > f1]

m1 and m2 are the surface densities of leaf 1 and leaf 2, respectively
f0 is the resonant frequency from the MSM resonant equation,
f1 is 55/d Hz
R1 and R2 are the transmission loss numbers you calculated first, using the mass law equation

And that's it! Nothing complex.
Nothing complex but what a lot of time this fascinating topic can eat up!

What is the aim of the f0? To be different to any of the modes? For example, if I have two lowest modes of 1-0-0 at 29Hz and 0-1-0 at 38Hz, should my aim be to get the f0 below 29Hz or is between them at 33 or 34Hz alright? Or, should the f0 be below audible frequencies, let's say below 10Hz?