## 2 Model Analysis
Within the specified parameter ranges, when the material's porosity exceeds 90%, the sound absorption performance remains relatively stable across different porosities, indicating that changes in porosity have a limited impact on sound absorption performance under these conditions. For glass-fiber-based porous materials, prior experiments have shown that under uniform material conditions, the pore size standard deviation remains below 0.3 and varies between 0.1 and 0.3. As observed in the figures, within this range, the NRC shows a gradual increase as the pore size standard deviation increases. Simultaneously, the peak sound absorption coefficient slightly decreases, while the mid-to-low frequency sound absorption coefficients slightly improve. Overall, the average sound absorption coefficient exhibits no significant change. However, a moderate broadening of the pore size distribution is beneficial for enhancing the mid-to-low frequency sound absorption performance of porous materials. Compared to porosity and pore size standard deviation, changes in median pore size have a more significant impact on sound absorption performance. The two-dimensional curves of sound absorption coefficients under changes in median pore size can be found in Figure S1. As the median pore size increases, the frequency of the first peak in the sound absorption coefficient shifts slightly toward higher frequencies, and the peak sound absorption coefficient first increases and then decreases. This indicates that under the same porosity and pore size standard deviation, smaller median pore sizes are beneficial for low-frequency sound absorption performance [3]. However, excessively small pore \begin{table}
\begin{tabular}{c c c c c c} \hline porosity & 0.90 & 0.92 & 0.94 & 0.96 & 0.98 \\ \hline median pore size (\(\upmu\)m) & 40 & 60 & 80 & 100 & 120 \\ \hline standard deviation in pore size distribution & 0.10 & 0.15 & 0.20 & 0.25 & 0.30 \\ \hline \end{tabular}
\end{table} 
Table 1: Ranges of different parameters. Figure 1: Finite element model diagram. sizes can lead to a reduction in overall sound absorption performance. This phenomenon occurs because smaller pore sizes result in a higher number of fibers per unit area, increasing the likelihood of sound waves colliding with the fiber surfaces within the material. Consequently, the friction between sound waves and the air within the material increases, prolonging the propagation time of the sound waves inside the material and converting a substantial amount of acoustic energy into thermal energy, leading to its dissipation. However, overly small pore sizes can significantly increase the material's density, leading to excessively high flow resistivity. This, in turn, causes a large amount of sound wave reflection, negatively affecting the acoustic performance of the material [40]. To intuitively demonstrate the impact of median pore size on sound propagation behavior, simulation results for representative frequencies in the low-, medium-, and high-frequency ranges--280 Hz, 800 Hz, and 2500 Hz--were compared. Figure 2g-i shows the scattered sound pressure fields in the absorption domain under different median pore sizes. In the scattered sound pressure maps, red and dark blue regions represent areas of high sound pressure [41], with color intensity reflecting the strength of sound wave energy. By comparing the scattered sound pressure fields at the same frequency but with different pore sizes, it can be observed that the degree of attenuation in scattered sound pressure varies. At low frequencies, smaller pore sizes result in weaker scattered sound pressures, indicating that at these frequencies, smaller pores lead to more complete absorption of the incident sound waves.