## 3 Results and Discussion
The peak's maximum shifted towards lower frequencies; thus, the improvement was at the expense of some sound absorption in the higher frequencies. Figure 11: Predicted relationship between thickness, \(h\), density, \(\rho\), and frequency after which the sound absorption coefficient begins to become larger than \(0.8,f_{0.8}\), for the considered RPU foams. Figure 12: Sound absorption coefficients for different air gap thicknesses, \(\rho\) = 40 kg/m\({}^{3}\). For example, at 500 Hz, h = 7 cm, and \(\rho\) = 40 kg/m\({}^{3}\), the sound absorption coefficient increased 66% when an air gap of d = 5 cm was introduced. For \(\rho\) = 55 kg/m\({}^{3}\), the sound absorption coefficient increased 38% and for \(\rho\) = 80 kg/m\({}^{3}\), the absorption coefficient increased 21%. However, at 1000 Hz, the sound absorption coefficients decreased when the air gap is introduced. For the RPUF with thickness h = 7 cm and density \(\rho\) = 40 kg/m\({}^{3}\), the introduction of air gap d = 5 cm shifted the peak's maximum from 1120 to 630 Hz (\(\Delta\)f = 490 Hz). This shifted peak created a region from 405 to 1160 Hz where the sound absorption coefficients were above 0.8. For the RPUF with thickness h = 7 cm and density \(\rho\) = 55 kg/m\({}^{3}\), the introduction of air gap d = 5 cm shifted the peak's maximum from 950 to 540 Hz (\(\Delta\)f = 410 Hz). The lowest frequency above which the sound absorption coefficient was above 0.8 was 328 Hz, and the value dropped to 0.80 at 1130 Hz. For the RPUF with thickness h = 7 cm and density \(\rho\) = 80 kg/m\({}^{3}\), the introduction of air gap d = 5 cm shifted the peak's maximum  
Figure 14: Sound absorption coefficients for different air gap thicknesses, \(\rho\) = 80 kg/m\({}^{3}\). Figure 7:0 Sound absorption coefficients for different air gap thicknesses, \(\rho\) = 55 kg/m\({}^{3}\). from 840 to 510 Hz ((Af = 330 Hz). The lowest frequency above which the sound absorption coefficient was above 0.8 was 280 Hz, and the value dropped to 0.84 at 1045 Hz. A comparison between several absorbing materials that are well established in the field of vibro-acoustics and the studied RPUFs is presented in Figure 7:1 These materials were measured in different laboratories using the impedance tube procedure. Since the thicknesses of the considered traditional acoustic materials range from 3 to 5 cm, only comparable RPUFs with thicknesses 4.5 cm and 7 cm were plotted. The RPUF with density \(\rho\) = 40 kg/m\({}^{3}\) and thickness h = 4.5 cm had lower values than the considered traditional acoustic materials, while the RPUFs with thickness h = 9.5 cm at all considered densities had superior values in the low to mid frequency region. Hence, these curves are not shown in Figure 7:2 Rock wool (RW) with thickness h = 5 cm and density \(\rho\) = 40 kg/m\({}^{3}\)[38] and melamine foam (MF) with thickness h = 5.1 cm and density \(\rho\) = 8.3 kg/m\({}^{3}\)[39] had comparable sound absorption coefficients with the RPUF with h = 4.5 cm and \(\rho\) = 55 kg/m\({}^{3}\) and the RPUF with h = 4.5 cm and \(\rho\) = 80 kg/m\({}^{3}\). Polyurethane foam (FU) with thickness h = 3 cm and \(\rho\) = 40 kg/m\({}^{3}\)[40] had comparable values with the RPUF with h = 7 cm and \(\rho\) = 40 kg/m\({}^{3}\). Glass wool (GW) [41] with h = 5 cm and \(\rho\) = 52 kg/m\({}^{3}\) was comparable to the RPUF with h = 7 cm and \(\rho\) = 55 kg/m\({}^{3}\), while the same sound absorption coefficients as GW at the lowest considered frequencies were achieved with the RPUF with h = 7 cm and \(\rho\) = 80 kg/m\({}^{3}\). The obtained results demonstrated that rebonded polyurethane foam can provide a good sound-absorbing material over a wide frequency range. This is enhanced by considering the fact that rebonded polyurethane foam is produced from waste, which is a sustainable concept and provides a low-cost product. As the humidity increases, the volume of the solid fraction of the material increases due to water absorption. An increase in temperature leads to an increase in the volume of the sample.