## 4 Results
### The Normal Incidence Sound Transmission Loss (Simulations)
The single-load method, for the numerical case when the model was perfectly geometrically symmetric, gave reasonably accurate data (comparable with the two-load method). The single-load method can be slightly affected by a high reflection of the termination (Figure 7f). In the worst case for the single layer membrane, the effect was not more than 0.7 dB at specific frequencies. The results obtained by means of the mobility-based method (MM) are presented in Figure 7d and a comparison with the ASTM method is shown in Figure 7e,f. In this comparison, the ASTM method with an absorption factor \(\alpha=1\) was chosen as a reference as this method gives most accurate results. As expected, the results obtained with the MM method are also affected by the multiple back/front reflections in the impedance tube. In case of an absorption of 20% at the impedance tube backing wall, differences up to 4 dB were observed compared to the ASTM (\(\alpha=1\))-reference method. Figure 7g present the structural and acoustic modes which influence the dips in the \(nTL\) spectra. In case of the circular (symmetrical) shaped specimens, only the symmetrical modes are influencing the resulting spectra. The acoustic modes are dependent on the length of the downstream. In order to demonstrate the applicability of the MM method to the modally slightly more complicated shape of membranes, the response of a rectangular membrane was numerically assessed. As in the previous case, a comparison of the results was made only between the ASTM and MM methods (Figure 8). The sound transmission loss and absorption of the rectangular membrane are most affected by the modes that have an odd number of half-wavelengths in the transverse direction of the membrane patch (Figure 8c). As in the previous cases, for the anechoic termination, the spectrum determined on the basis of both methods correlates well with each other in a global sense. Exceptions  
Figure 7: The \(nTL\) of 0.5 mm thin membrane determination by means of different methods from the FEM model for six different backing wall sound-absorption terminations (variation of termination absorption from \(\alpha\)=0.1 to 1). (**a**) [PERSON] (Wave field decomposition method (WD)—one load); (**b**) [PERSON] (WD-TM hybrid method—two loads variations with termination (“term.” in the legend) absorptions denoted as \(\alpha_{1}\),\(\alpha_{2}\) for first load and second load); (**c**) ASTM E261109 (“ASTM” in the legend, Transfer matrix method—single or two-load variations with different termination absorptions denoted as \(\alpha_{1}\),\(\alpha_{2}\) for first load and second load variations); (**d**) mobility based method (MM—single load); (**e**) comparison of methods; (**f**) comparison of chosen cases by the difference in the frequency spectra (\(\Delta nTL=nTL_{i}-nTL_{ASTM\,\,\alpha=1}\)); and (**g**) \(nTL\) spectra of calculated based MM, with termination \(\alpha=0.1\). The figure also includes structural modes of the membrane as well as the acoustic modes of downstream tube causing the resonant phenomena in the spectrum. occur at specific frequencies which are related to resonances and anti-resonances. Here, visible deviations up to 3 dB occur from the second mode having an odd number of half wavelengths (Figure 8c). Paradoxically, this deviation, as in previous cases of anechoic terminations of the MM method, is due to the fineness of the datapoint mesh on the membrane surface. This can distort the attenuation in the resonant phenomenon. By increasing the reflectivity of the backing wall termination, the front-back reflection in the form of additional peaks in the spectrum is more pronounced.