## 4 Results
### The Normal-Incidence Sound Absorption and Transmission Coefficients (Simulations)  
The normal incidence sound absorption and transmission coefficients were determined by means of two techniques. The first one, the reference method, was the TFM in accordance with ISO 10534-2. The second method, the mobility method, included the surface spatial averaged displacement in the normal direction to the surface (in figures denoted as the  
Figure 8: 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 (“term.” in the legend) absorption from \(\alpha\) = 0.1 to 1) (**a**) 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); (**b**) mobility based method (MM—single load); (**c**) comparison of methods including graphical representation of resonant phenomena causing decreases in the spectrum.; and (**d**) comparison of chosen cases by the difference in the frequency spectra(\(\Delta nTL\) = \(nTL_{i}-nTL_{ASTM\ \alpha=1}\)).  
mobility-based method--MM). The comparison of results is shown in Figures 9 and 10. One can see that the results are in both cases dependent on the sound absorption of the impedance tube termination (as expected). For a fully anechoic termination, almost the same results were obtained for both methods. However, reducing the absorption coefficient of the downstream termination the difference of the resulting absorption has increased up to \(\Delta\alpha=1(\%)\) to \(1.5(\%)\), respectively, where \(\Delta\alpha=(\alpha-\tau)\cdot 100\%\), at frequencies of the membrane symmetrical mode resonances. By using the parametric study, one can simply distinguish between the membrane resonance caused absorption/transmission coefficient peaks, the downstream tube termination cased resonances (strong effect in case of single membrane--the increasing effect is visible by increasing the reflection of the termination) (Figure 9a,b).  
Figure 9: Normal-incidence sound absorption of a single leaf PTFE membrane determined for six different terminations (variation of termination (“term.” in the legend) absorption from \(\alpha=0.1\) to \(1\), data were obtained from FEM). (**a**) TFM-ISO 10534-2 (“ISO” in the legend); (**b**) mobility-based method (“MM” in the legend); and (**c**) difference between sound absorption obtained by means two methods expressed in percentage.  
For a rectangular membrane (Figure 10), resonances caused by downstream front-back reflection are strongly suppressed except for the first mode of the tube, as it occurs near the 3 rd and 6 th odd membrane modes. The difference in spectra between the individual methods is, unlike the transmission loss (logarithmic expression), expressed as a percentage. Here, again, depending on the type of tube termination, the resonant response manifested in the peak/dip spectrum increases. The deviation with anechoic termination in comparison with MM with the ISO method reaches a deviation of up to 3.5% for the second odd mode and below 1% for other modes, what is acceptable. Interestingly, by changing the shape of the membrane and the associated distribution of resonant modes, an increase in the sound absorption of the sample was achieved.