The Impedance and the Absorption of Acoustical Materials to Sound at Random Incidence

Abstract

The boundary value problem of an infinite sheet of homogeneous acoustical material with hard backing has been set up and solved for random incidence sound. This leads to an equation for the random coefficient similar to that of Paris, except it uses, instead of the normal impedance, the impedance of the normal component which varies with angle. The admittance of the normal component is given by Y(θ)ρc = χ tanhγ1′l = iρcγ1′ tanhγ1′lωρ1′, where γ1′ = (α2 − β2 + ω2c2 sin2θ − 2iαβ)12, α and β are the propagation constants, and ρ1′ is a complex density of the medium equal, in the case of viscous damping, to ρ1[1 + i(R/ωρ1)], where R is the damping constant in dyne sec cm−4. Check with experiment, however, indicates that viscous damping is only a partial explanation of the attenuation mechanism. Even with the latter uncertainty, the propagation constants and the characteristic admittance χ can be computed by the method of Ferrero and Sacerdote. The propagation constants calculated from the above check with those given by Esmail-Begui and Naylor. The random coefficient calculated by theory agrees well with that measured in reverberation room and explains quantitatively the large discrepancy between the “statistical” and reverberation coefficient for light density materials.