## 4 Results and Discussion
### Sound Transmission Loss Predictions and Measurements  
For the prediction of the transmission coefficient \(\tau(\varphi)\) through Equation (6), the loss factor must be determined. To this aim, structural reverberation time measurements have been carried out in twelve measurement positions (Figure 7a) while the panel was mounted in the opening dividing the two reverberation rooms. The loss factor has been computed by the formula [33]:  
\[\eta=\frac{2.2}{f_{1/3}T_{R}} \tag{15}\]  
Once the average of the structural reverberation time (\(T_{R}\)) for each one-third octave band of interest (\(f_{1/3}\)) was computed it was possible to estimate the loss factor for the mounting conditions adopted during the measurements. The resulting loss factor is shown in Figure 7b.  
Figure 8 shows the comparison between the sound transmission loss based on the orthotropic bending stiffness function in Equation (7) (solid line) and the result of reverberation rooms  
Figure 6: Apparent bending stiffness per unit width of the sandwich panel (solid line) obtained from the experimentally-determined bending stiffnesses in the \(x\)-direction (circle markers) and in the \(y\)-direction (asterisk markers).  
Figure 7: Determination of the loss factor. (**a**) Measurement positions over the panel tested in reverberation rooms. (**b**) Resulting loss factor as a function of frequency.  
measurements according to ISO 10140-2 (dotted line). It can be observed that the agreement at and around the critical region is good, since both the location of the coincidence frequency and the \(STL\) value are predicted correctly. However, at lower frequencies, the measured \(STL\) values are considerably higher than the \(STL\) resulting from the transmission coefficient computed according to Equation (6). This is due to the fact that the latter describes the behavior of an infinite panel, while the panel measured in the reverberation rooms has finite dimensions. In the case of an infinite panel, the bending waves propagate in every direction without being reflected by the boundaries. In real, finite-size panels, the bending waves are reflected at the boundary and give rise to a sound radiation which can be considered the sum of a resonant and a non-resonant behavior. The resonant behavior takes place at frequencies above the critical region, where the entire plate radiates, and the contribution of the non-resonant field is negligible compared to that of the resonant modes. The non-resonant radiation of the plate is only significant at frequencies below the coincidence, at which sound is radiated by areas where cancellation between nodes and anti-nodes arising from standing waves is ineffective. The non-resonant transmission coefficient \(\tau_{NR}\) according to [PERSON] et al. [48] can be computed as:  
\[\begin{array}{c}\tau_{NR}=\left(\frac{2\rho_{0}}{\mu\,k_{air}\left(1-F^{-4} \right)}\right)^{2}\{\ln\left(k_{air}\sqrt{L\times H}\right)+0.160-U(L/H)\\ +\frac{1}{4\,F^{6}}\{\left[\left(2F^{2}-1\right)\left(F^{2}+1\right)^{2}\ln \left(F^{2}-1\right)\right.\right.\\ \left.\left.+\left(2F^{2}+1\right)\left(F^{2}-1\right)^{2}\ln\left(F^{2}+1 \right)-4F^{2}-8F^{6}\ln F\right]\}\end{array} \tag{16}\]  
where \(F=(f_{c}/f)^{1/2}\), \(k_{air}\) is the frequency-dependent wavenumber in air, and \(U\), which is a function of the panel's aspect ratio (\(L/H\)), is ignored when (\(L/H\)) is between 1/3 and 3 [49], as in the case at hand.  
The dashed line in Figure 8 represents the sound transmission loss calculated from the non-resonant transmission coefficient \(\tau_{NR}\). The agreement with the results from the measurement carried out in reverberant rooms is fair.