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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 travelling 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 dB

My 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 travelling 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 dB

My 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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