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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?
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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