## 3 MPP Samples
### Specim Properties  
Three different SL configurations were measured, one for every type of sample (MPP01, MPP02, MPP03). A different value of the air cavity thickness was chosen for every MPP sample, in order to obtain a good sound absorption peak around 1000 Hz. The same was done for four different DL configurations, composed of the type of samples mentioned above. Two layers of MPP provide two different resonance peaks: the choice was to try to find DL configurations with an absorption peak at 1000 Hz and a second peak in a lower frequency range. The three samples had the effective geometrical parameters reported in Table 3.  
The comparison between the equivalent fluid model and the experimental measurements is reported in terms of sound absorption coefficient and normalized surface impedance in Figure 11 for three SL configurations. The three samples were used in four different combinations of DL configurations with air cavities reported in Table 4, and a comparison was made between the EF model and the experimental measurements in terms of sound absorption coefficient and normalized  
Figure 10: Electro-acoustical equivalent circuit for SL-MPP and DL-MPP configurations: the inductance \(L_{comp}\) is in parallel with the MPP surface impedance \(Z_{MPP}\), and the resistance \(R_{comp}\) is in series with \(Z_{MPP}\). surface impedance in Figure 12. In contrast to the SL comparisons, the DL experimental measurements showed bigger discrepancies from the model: this is due to the mounting procedure inaccuracies and the irregular perforations of two different samples, both doubled. The model compensation is not enough to completely compensate for the non-idealities, mainly in terms of normalized surface impedance. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**1 st Cav.**} & \multicolumn{2}{c}{**2 nd Cav.**} & \multicolumn{4}{c}{\(\boldsymbol{\zeta}\)} \\  & \multicolumn{2}{c}{**2 nd Layer**} & \multicolumn{2}{c}{**2 nd Layer**} & \multicolumn{2}{c}{**125 Hz**} & \multicolumn{2}{c}{**250 Hz**} & \multicolumn{2}{c}{**500 Hz**} & \multicolumn{2}{c}{**1 kHz**} & \multicolumn{2}{c}{**2 kHz**} & \multicolumn{2}{c}{**4 kHz**} \\ \hline A & MPP01 & 40 & MPP01 & 30 & \(1.3-16.4i\) & \(1.3-6.8i\) & \(1.8-0.9i\) & \(2.2+2.0i\) & \(1.6+8.4i\) & \(4.4+ai\) \\ B & MPP01 & 50 & MPP02 & 50 & \(1.4-12.3i\) & \(1.5-4.9i\) & \(1.9-0.1i\) & \(2.5+2.7i\) & \(1.8+9.0i\) & \(3.1-ai\) \\ C & MPP02 & 45 & MPP03 & 45 & \(0.4-14.2i\) & \(0.4-6.2i\) & \(0.7-1.4i\) & \(1.7-0.4i\) & \(0.5+3.5i\) & \(1.8+8.5i\) \\ D & MPP01 & 35 & MPP03 & 35 & \(1.4-18.1i\) & \(1.4-7.7i\) & \(1.5-1.6i\) & \(3.1+2.3i\) & \(1.8+7.5i\) & \(2.1+15.7i\) \\ \hline \hline \end{tabular} \(a\rightarrow\infty\): the function diverges to infinity or minus infinity.  
\end{table} 
Table 4: Specific normalised impedances corresponding to the four double-layer configurations. Octave band data were fitted based on the outcomes of the compensation model described in the text. Figure 11: Sound absorption coefficient and normalized surface impedance of single-layer MPPs: MPP01 with an air cavity of \(D=14.8\) mm, MPP02 with an air cavity of \(D=30\) mm and MPP03 with an air cavity of \(D=20\) mm. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multicolumn{2}{c}{**MPP01**} & \multicolumn{2}{c}{**MPP02**} & \multicolumn{2}{c}{**MPP03**} \\ \cline{2-7}  & \multicolumn{2}{c}{**Exp.**} & \multicolumn{2}{c}{**Eff.**} & \multicolumn{2}{c}{**Exp.**} & \multicolumn{2}{c}{**Eff.**} & \multicolumn{2}{c}{**Exp.**} & \multicolumn{2}{c}{**Eff.**} \\ \hline Thickness (mm) & 1 & 0.94 \(\pm\) 0.03 & 1 & 0.95 \(\pm\) 0.01 & 1 & 0.92 \(\pm\) 0.02 \\ Porosity (\%) & 0.5 & 0.5 & 1 & 1 & 0.5 & 0.5 \\ Perforation & 0.5 & 0.483 \(\pm\) 0.04 & 0.5 & 0.482 \(\pm\) 0.03 & 0.3 & 0.33 \(\pm\) 0.05 \\ diameter (mm) & 0.5 & 0.483 \(\pm\) 0.04 & 0.5 & 0.482 \(\pm\) 0.03 & 0.3 & 0.33 \(\pm\) 0.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Expected (exp.) and effective (eff.)