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

284 12. Walls, Enclosures, and Barrierscorrelate the panel velocity with the transmitted particle velocity:cos θu panel = p Tρc .Using the last of the Equation set (12.5) in the preceding expression and differentiatingwith respect to time, we now obtainik(ct−x cos θ−y sin θ) cos θa panel = ikcP T eρc= iωP T cos θ.ρcInserting the above expression into Equation (12.9) and applying Equations (12.5)at the panel, where x = 0, the amplitudes of the pressures are related to each otherbyP I + P R − P T = imωP Tcos θ. (12.10)ρcThe pressure term P R in Equation (12.10) may now be eliminated through the useof Equation (12.8). The ratio of transmitted pressure amplitude to incident pressureamplitude may now be obtained asP TP I=1.imω cos θ1 +2ρcWe now express the sound transmission coefficient asτ = p2 rms(T )p 2 rms(I )= |P T | 2|P I | 2 = 1( ) imω cos θ 2.1 +2ρcFrom the definition of Equation (12.3), we obtain the mass law transmission lossequation:( ) [ ( ) ]1 mω cos θ2TL = 10 log = 10 log 1 +. (12.11)r 2ρcSetting the angle of incidence equal to zero, Equation (12.11) reduces to[ ( ) ]mω2TL 0 = 10 log 1 +(12.12)2ρcwhich constitutes the statement for the normal incidence mass law for approximatingtransmission loss of panels with sound at 0 ◦ angle of incidence.12.4 Field Incidence Mass LawIn the situation of transmission loss between two adjoining rooms, the sound sourcein one room may produce a reverberant field. The incident sound emanating from