Sound isolation capacity of an idealized wall construction

AI Thread Summary
The discussion focuses on estimating the sound isolation capacity of a wall structure, emphasizing the importance of wall impedance, mass, and rigidity in sound isolation. The user has calculated wall impedance using specific parameters for a gypsum board wall and is questioning the accuracy of their results. They have derived values for impedance based on mass and rigidity, yielding different sound isolation levels in decibels. The user seeks guidance on whether their calculations are correct and what steps to take next for further analysis. Understanding these factors is crucial for evaluating the sound isolation quality of wall constructions.
sigertdejean
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I'm looking to understand how to estimate the sound isolation capacity of a wall structure. With rising degree of detail will probably come an exponantial increase in complexity. I'm looking to start of, euhm,... gently. :shy:
What I've gathered so far:
-The impedance of the wall seems to take center stage
-There's atleast two fundamental aspects of the wall that govern its sound isolating qualities: mass and rigidity, each dominant over the other in a different frequency range

I've posted one of the equations I've tried to solve, hoping someone can shine a light.
A plane wave of single frequency 200Hz traveling through air at 344m/s is obstructed by a single leaf gypsum board wall, 25mm thick, with infinite X and Y dimensions (some wall eh).

Frequency f = 200Hz
Thickness h = 0.025 m
Young’s modulus E = 2,3*10^9 N/m²
Poisson ratio V = 0,33
Mass M = 25 Kg/m²
Speed of sound c = 344 m/s
Angle of incidence φ = Perpendicular to boundary = 1/2π

w = f * 2π
= 200Hz * 2π
= 400π

Rigidity D = (E*h³)/(12*(1-V²))
= (2,3*10^9*0.025³)/(12*(1-0.33²))
= 3360,78

Z = M*w² (wall impedance as a result of its Mass)
= 25*(400π)²
= 39478417,6
=> 20*LOG(39478417,6) = 151,93 dB

Z = D*((w / c)*sinφ)^4 (wall impedance as a result of its Rigidity)
= 3360,78*((200Hz*2π / 344)*sin (1/2π))^4
= 3360,78*(400π / 344)^4
= 598474,66
=> 20*LOG(598474,66) = 115,54 dBMy questions:
1) Are my numbers really off, or is it just me?
2) Assuming I get the impedance right, what would be the next step in determining the sound isolation quality of this idealized wall structure?
 
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