## 3 Results and Discussion
For the RPU foam with thickness h = 2 cm and density \(\rho\) = 40 kg/m\({}^{3}\), a sound absorption coefficient above 0.8 was not achieved in the considered frequency region and for \(\rho\) = 80 kg/m\({}^{3}\), a sound absorption coefficient above 0.8 was achieved after 2630 Hz, i.e., even for the highest considered density, the sample with thickness h = 2 cm had low sound absorption. Observing the samples with thicknesses of 6 and 8 cm, for the RPUF with density \(\rho\) = 40 kg/m\({}^{3}\), the shift of the peak's maximum was from 1355 to 960 Hz (\(\Delta\)f = 395 Hz), i.e., from \(\lambda\)/h = 4.22 to \(\lambda\)/h = 4.47, where \(\lambda\) = 343/f is the acoustic wavelength. For RPUF with density \(\rho\) = 55 kg/m\({}^{3}\), increasing the thickness from 6 to 8 cm moved the maximum of the peak from 1135 to 800 Hz (\(\Delta\)f = 335 Hz), i.e., \(\lambda\)/h = 5.04 to \(\lambda\)/h = 5.36. For \(\rho\) = 80 kg/m\({}^{3}\) the shift was from 995 to 730 Hz (\(\Delta\)f = 265 Hz), i.e., from \(\lambda\)/h = 5.75 to \(\lambda\)/h = 5.87. The coefficient \(\lambda\)/h for the considered RPUFs increased with increasing density and thickness and became higher than 4, i.e., the speed of sound in the porous material became lower than the speed of sound in air [17]. In addition, the shifting range decreased with increasing density. In order to estimate the frequency after which the sound absorption coefficient became larger than 0.8, \(f_{0.8}\), for a given thickness [m] and density [kg/m\({}^{3}\)] of the RPUF, a polynomial surface model with x degree of 4 and y degree of 2 was fitted to the predicted data for a range of thicknesses h = 0.04-0.13 m and considered densities \(\rho\) = 40 kg/m\({}^{3}\), \(\rho\) = 55 kg/m\({}^{3}\), and \(\rho\) = 80 kg/m\({}^{3}\). The root mean square error for the fitted polynomial surface was RMSE = 16.1. The results are graphically presented in Figure 11. The densities \(\rho\) = 50 kg/m\({}^{3}\), \(\rho\) = 60 kg/m\({}^{3}\), and \(\rho\) = 70 kg/m\({}^{3}\) are included. This graph can help to quickly estimate the starting frequency of good sound absorption for the considered RPUFs. After \(f_{0.8}\), the sound absorption coefficients ranged between 0.8 and 1 for all thicknesses, except for h = 4 cm where a slight drop below 0.8 occurred in a very limited frequency region. Figure 10: Calculated sound absorption coefficients for RPU foams with different thicknesses. According to Figure 11, in order to achieve a sound absorption coefficient greater than 0.8, starting from the 500 Hz, thicknesses of h\({}_{0.8}\) = 6.7 cm, h\({}_{0.8}\) = 6.8 cm, h\({}_{0.8}\) = 7.3 cm, h\({}_{0.8}\) = 8.1 cm, and h\({}_{0.8}\) = 9.1 cm were required for \(\rho\) = 80 kg/m\({}^{3}\), \(\rho\) = 70 kg/m\({}^{3}\), \(\rho\) = 60 kg/m\({}^{3}\), \(\rho\) = 50 kg/m\({}^{3}\), and \(\rho\) = 40 kg/m\({}^{3}\), respectfully. This result has a logical sequence in relation to the obtained measurements (Figure 6) since the sound absorption coefficient was 0.83 for \(\rho\) = 80 kg/m\({}^{3}\) and h = 7 cm, and 0.86 for \(\rho\) = 40 kg/m\({}^{3}\) and h = 9.5 cm. The ratio of the acoustic wavelength of 500 Hz and needed thickness h\({}_{0.8}\), \(\lambda\)/h\({}_{0.8}\), ranged between 10.24 and 7.54. Hence for lower densities, i.e., for 60 kg/m\({}^{3}\) and lower, the well-known criterion h-\(\lambda\)/10 will not be sufficient to achieve a sound absorption coefficient of 0.8 for 500 Hz. The predicted curves for \(\rho\) = 70 kg/m\({}^{3}\) and \(\rho\) = 80 kg/m\({}^{3}\) converged above thickness h = 7.5 cm. The effect of including an air gap between the porous layer and the wall was also investigated. Four different thicknesses of the air gap were considered, d = 0 cm, d = 5 cm, d = 8 cm, and d = 10 cm. The introduction of the air gap led to improved sound absorption in the low to mid frequency range (Figures 12-14), with very similar results as increasing the thickness.