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Attenuation in a chamber can be expressed as
dL = 10 log( 1 / Ao (cosθ / 2 π s2 + (1 - α) / (α A)) ) (1)
where
dL = sound attenuation (dB)
Ao = outlet area (m2)
A = chamber inside surface area (m2)
θ = angle between inlet and outlet (degrees)
s = distance between inlet and outlet (m)
α = inside surface sound absorption coefficient
The attenuation in a chamber lined with mineral wool with a sound absorption coefficient α = 0.65, inside surface area A = 16 m2, outlet area Ao = 0.25 m2, distance between inlet and outlet s = 2 m, angle between inlet and outlet α = 45o, can be calculated as
dL = 10 log( 1 / (0.3 m2) (cos45o / 2 π (2 m)2 + (1 - 0.65)/(0.65 (16 m2))) )
= 17.3 dB
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