JASA-51-3 Part I-1972

Received 6 July 1971 2.9 Sound Transmission through a Double-Leaf Wall R. J. DotqAXO Building hysics ection, ivision f Building Research, ational Research ormoil f Canada, tt awa, anada The classical pproach o the calculation f sound ransmission oss hrough ouble-leaf alls s reformu- lated and various evices mployed o reduce heresulting ntegrals o a tractable ormforanalytical solution. n approximation s made t low requencies hereby, sing transform echnique, he inite size f the wall may be ncluded. omparisons ith experimental easurements how ood greement ith theoretical redictions. INTRODUCTION There are essentially wo method s or calculating the sound ransmission oss hrough a double-leaf wall. The classical pproach hosen y London and Beranek and Work 2 uses he easily derived formulas or transmission t a fixed angle of incidence nd then sums over all possible ncident angles. These authors found the resulting ntegrals o be too intractable or analytical solution and computed the transmission oss numeri- cally. The other method is the statistical mechanical approach adopted by White and Powell, who use the ideasof Lyon and Maidanik in considering nergy flows betweentwo or more coupled multiresonant systems s an analog of a heat transmission roblem; the analog of temperature s the modal energy. his technique has the advantage of considering inite radiatorsnd vibrators, hereas he classical pproach deals with infinite area components. From a practical point of view, the requirement s for an analysis h at will show he contributions f the various parameters to the transmission loss. For instance, he effect of wall spacing s not readily seen from the analysis f White and Powell. This is partly due to a doubtful eature n the analysis. hese authors take the power flow between systems and s to be R/(S,•--S,u), where R, ß is the nondissipative gyro- scopic) oupling esistance etween he systems, nd S v is the velocity spectral ensity. This is at variance with Lyon and Scharton • and Eichler, who take the power flow to be proportional to (•n,'S, •-•,'S,•), where n,'= R.'/•M,, and S s is the energy spectral density. White assumes that R,'=R/, which allows R/S•'--R,•S,• to be written as R/(S,'--S/). On the other hand Eichler writes the equation of power flow between he two systems as where V is veloc ity. f we take systems f equal modal densit)', then becanse ,•7,•--n•v/, where •r, no are the modal densities in this case equal), there is no power flow when S•=S, •' or M',V?=M,V, •, whereas White and Powell say there is no power flow when V?=V, •. Further, if •/=•,', then Clearly, then, the relationship between must include the modal masses as well as modal densities s n,•,'=n•l/, where n is th e modal density2 a This possibly ccounts or the absence f any term representing he panel spacing n the derivation of White and Powell. a Even without this objection one still has to make use. For the externally radiated po wer one ma y use Maidanik's expression, but there is still doubt ab out the correct value to use for energy radiated into the cavity. White and Powell use a value equal to twice the external adiation mpedanc% ut this is probably only true below coincidence . A later paper by Price and Crocker applies these techniques o the double-wall roblem? Although he results are impressive, here still remain a few pecul iar- ities. Whil e the results agree well with our own experimental ones for a double wall having an absorbing layer, the results o not agree with those or an absorp- tion-free space, he discrepancies eingaround15-20 dB. Further, these authors how he effect of varying The Journal of the Acousticalociety of A merica 807 ded 23 Dec 2010 to 200.23.51.1. Redistribution subject to ASA license or copyright; see http://asadl.org/journals/doc/ASALIB-home/info/te

JASA-51-3 Part I-1972

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Transcript of JASA-51-3 Part I-1972