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Sound isolation capacity of an idealized wall construction

  1. Apr 10, 2009 #1
    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?
     
    Last edited: Apr 11, 2009
  2. jcsd
  3. Apr 16, 2009 #2
  4. Apr 23, 2009 #3
    Another forum perhaps?
     
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