THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

an ideal gas) varies in the following manner:12.7 The Double-Panel Partition 291pv γ = constant (12.19)where v represents the specific volume (equal to the reciprocal of density) and γ ,the ratio of specific heats. Differentiating Equation (12.19) givesdpdv =−γ p v . (12.20)Sound waves cause the ambient pressure and specific volume of air to vary onlyslightly from the quiescent values of p 0 and v 0 , and thus the instantaneous valuesp and v differ very little from p 0 and v 0 in Equation (12.20). Because the massof air entrapped between the panels remains constant, the ratio of panel displacement(arising from the sound pressure pushing on the panels) dh to the original(quiescent) spacing h 0 should equal the ratio of the change of specific volume tothe quiescent value of the specific volume:dh= dv(12.21)h 0 v 0But the spring constant represents the force per unit displacement, or for a unitarea of the wallk =− dpdh . (12.22)Combining Equations (12.21) and (12.22) and dropping the subscripts (sinceh 0 ≈ h, p 0 ≈ p), we now havek =− γ phwhich, upon inserting into Equation (12.19), gives√γ p m 1 + m 2hmf n =1 m 2.2πSetting γ = 1.4 and p = 101.325 kPa (the standard atmosphere), the lowfrequencyresonance of the double-panel wall may now be found from√m1 + mf n = 602. (12.23)hm 1 m 2The surface masses m 1 and m 2 are given in kg/m 2 and the panel spacing h inmeters.Example Problem 2Predict the transmission loss for an 8-in. wall of poured concrete for 800-Hz sound.The concrete has a density of approximately 150 lb/ft 3 (2406 kg/m 3 ).