## 5 Experimental Validation of the Optimal Combination Structure
The difference reached 15.8652% and 18.922%, respectively, when the limited total thickness was 30 mm and 50 mm. On the contrary, for the sound absorber of porous metal, the difference was 5.8649% and 10.6585%, respectively, when the limited total thickness was 30 mm and 50 mm. A major reason for this may be that it was difficult to fabricate a microperforated panel completely consistent with its structural parameters, with the fabrication error being determined by the processing capability and kinematic accuracy of the manufacturing equipment. Moreover, the vibration of the microperforated panel under acoustic excitation could result in errors as well. These phenomena would certainly affect the two combination structures. When the limited total thickness was 30 mm and 50 mm, for the porous metal + cavity + microperforated panel + cavity sound absorber, the difference was 15.8652% and 16.673%, respectively; for the microperforated panel + cavity + porous metal + cavity sound absorber, the difference was 8.4739% and 6.6595%, respectively. Though there existed deviations between the theoretical and experimental data for the four investigated sound absorbers, a novel method to develop low frequency sound absorbers by parameter optimization was proposed and validated. Figure 7: Comparisons of theoretical data, simulation data, and experimental data with the limited total thickness of 50 mm. (**a**) Porous metal + cavity + microperforated panel + cavity; (**b**) Microperforated panel + cavity + porous metal + cavity; (**c**) Porous metal + cavity; (**d**) Microperforated panel + cavity. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Acquisition Mode** & \begin{tabular}{c} **Porous Metal + Cavity +** \\ **Microperforated Panel + Cavity** \\ \end{tabular} & \begin{tabular}{c} **Microperforated Panel + Cavity +** \\ **Porous Metal + Cavity** \\ \end{tabular} & \
\begin{tabular}{c} **Porous Metal +** \\ **Cavity** \\ \end{tabular} &
\begin{tabular}{c} **Microperforated** \\ **Panel + Cavity** \\ \end{tabular} \\ \hline Theoretical analysis & 65.0575\% & 71.4354\% & 44.7572\% & 65.0575\% \\ Finite element simulation & 65.1137\% & 69.8007\% & 40.5819\% & 65.1137\% \\ Experimental measurement & 49:1923\% & 62.9615\% & 38.8923\% & 49.1923\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The average sound absorption coefficients when the limited total thickness was 30 mm. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Acquisition Mode** & \begin{tabular}{c} **Porous Metal + Cavity +** \\ **Microperforated Panel + Cavity** \\ \end{tabular} & \begin{tabular}{c} **Microperforated Panel + Cavity +** \\ **Porous Metal + Cavity** \\ \end{tabular} & \
\begin{tabular}{c} **Porous Metal +** \\ **Cavity** \\ \end{tabular} &
\begin{tabular}{c} **Microperforated** \\ **Panel + Cavity** \\ \end{tabular} \\ \hline Theoretical analysis & 74.6653\% & 80.2518\% & 70.7277\% & 73.4605\% \\ Finite element simulation & 70.6537\% & 78.8461\% & 69.8066\% & 73.4642\% \\ Experimental measurement & 57.9923\% & 73.5923\% & 60.0692\% & 54.5385\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The average sound absorption coefficients when the limited total thickness was 50 mm.