ALtl = A LTL1 + A LTL2 + 20 log (2 k d) f0 > f > f (9.48)

where A Ltl1 and A Ltl2 are the mass law transmission losses for each panel. Each term in Eq. 9.48 increases 6 dB per octave so the overall transmission loss rises 18 dB per octave in this frequency range. It also increases 6 dB for each doubling of the separation distance between the panels. At still higher frequencies resonant modes can be sustained in the airspace between the panels and there arises a series of closed tube resonances, normal to the surfaces, having frequencies fn = nd° forn = 1' 2' 3 ••• (9.49)

These aid in the transfer of sound energy between the panels and result in a series of dips in the double-panel transmission loss, shown in Fig. 9.16. Due to the damping provided by batt insulation, we usually do not see this pattern in actual transmission loss measurements, which are carried out in third-octave bands. Batt flattens out the slope of the transmission

Figure 9.16 Theoretical Transmission Loss of an Ideal Double Panel (Sharp, 1973)

Figure 9.16 Theoretical Transmission Loss of an Ideal Double Panel (Sharp, 1973)

loss curve from 18 dB/octave down to 12 dB/octave in this region. The transmission loss behavior above a limiting frequency is given by

The crossover frequency, which can be obtained by setting Eq. 9.48 equal to Eq. 9.50, is equal to the first cavity resonance frequency divided by n.

Equations 9.46,9.48, and 9.50 give the transmission loss of an ideal double panel system in three frequency ranges separated by the frequencies in Eqs. 9.42 and 9.51. Measurements by Sharp (1973) have shown that there is good agreement between theoretical and measured data for both the mass-reactance region (Fig. 9.17) and the critical region (Fig. 9.18). The panel transmission loss values in the critical region were used instead of simple mass law predictions.

Cavity Insulation

The theory that has been developed here has assumed that the air cavity is well damped. When there is no absorptive material between the panels, cavity resonances contribute to the transmission of sound from one side to the other in much the same way as a mechanical coupling would. The addition of damping material such as fiberglass batt insulation attenuates these modes. Figure 9.19 (Sharp, 1973) shows the effects of a fully isolated double-panel system, with and without batt insulation. The panels used were 1/4" and 1/8" hardboard so that the coincidence frequencies were above the frequency range of interest. Below the first

Figure 9.17 Measured and Calculated Transmission Loss Values for a Separated Double Panel (Sharp, 1973)

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