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

12.5 Effect of Frequencies on Sound Transmission through Panels 285the source may strike the wall at all angles between 0 and 90 ◦ . For field incidenceit is customary to assume that the angle of incidence lies between 0 and 72˚, whichresults in a field incidence transmission loss of approximatelyTL = TL 0 − 5dB.We can modify the mass law equation by converting the angular frequency ofsound (rad/s) into cyclic frequency (Hz), i.e. ω/2π = f , by setting the acousticimpedance for air ρc = 407 rayls, and assuming mω/(2ρc) ≫ 1. This gives thefield incidence mass law equationTL = 20 log( fm) − 47 dB (12.13)where m denotes the mass per unit area (kg/m 2 ).Equation (12.13) indicates for the mass-controlled frequency region that transmissionloss of a panel increases by 6 dB per octave, Doubling either the panelthickness or the density of the panel will also engender an additional 6 dB loss for agiven frequency. While Equation (12.13) is useful for the prediction of a material’sacoustical behavior, laboratory or field testing should be conducted to measure thetransmission loss of actual structures under real environmental conditions.Example Problem 1A wall is considered to have its sound transmission mass-controlled. Plot thetransmission loss as a function of the product of frequency and mass per unit area.SolutionUsing Equation (12.13), which expresses the field incidence mass law for typicalconditions, we can writeTL = 20 log( fm) − 47 dB.For the normal incidence mass law:TL = 20 log( fm) − 42 dB.Figure 12.2 shows the semilog plot of both relationships as two straight lines. Itshould be noted here that these values tend to be considerably higher than thoseof the actual transmission losses.12.5 Effect of Frequencies on Sound Transmissionthrough PanelsPanel bending stiffness constitutes the governing factor in low-frequency soundtransmission. The panel resonances play the principal role in determining thenature of transmission of higher frequency sounds. The panel may be consideredmass-controlled in the frequency range from twice the lowest resonant frequencyto below the critical frequency (discussed below).