## 4 Simulation Study on Foam Acoustic Parameters
### Effect of Foam Porosity on Acoustic Radiation Performance  
Porosity is a parameter that characterizes the proportion of internal pore space within porous materials, as shown in Equation (2) [21]. Porosity not only affects the acoustic radiation performance of foam materials but increasing the porosity of foam materials can also reduce their thermal conductivity, thereby improving their thermal insulation performance [22].  
\[\phi=\frac{V_{a}}{V_{t}}=1-\frac{V_{m}}{V_{t}}, \tag{2}\]  
here \(\phi\) signifies the porosity of the porous material, \(V_{a}\) denotes the air volume within the porous material, \(V_{t}\) stands for the total volume of the porous material, and \(V_{m}\) represents the volume of the porous material's framework.  
Keeping all other parameters constant, the foam porosity is set to 0.99, 0.97 (the original value), 0.95, 0.93, and 0.91. The radiated power at various porosities is calculated, and Figure 11 displays the results.  
According to Table 4, at 854 Hz, the sound power levels increase from low to high porosities at 40.73 dB, 40.63 dB, 40.54 dB, 40.44 dB, and 40.35 dB. Correspondingly, at 1467 Hz, the levels at low to high porosities are 17.81 dB, 17.80 dB, 17.79 dB, 17.78 dB, and 17.77 dB. Similarly, at 1588 Hz, the levels at low to high porosities are 42.53 dB, 42.50 dB, 42.46 dB, 42.42 dB, and 42.38 dB. Calculations based on the above data show that a 1% increase in porosity at 854 Hz, 1467 Hz, and 1588 Hz leads to a decrease in radiated sound power levels by 0.0475 dB, 0.005 dB, and 0.01875 dB, respectively. It is clear that altering the porosity alone has a negligible impact on the sound-radiating performance and can be disregarded.  
\begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Peak Frequency** & **Sound Power Level** \\ \hline \multirow{3}{*}{87,000 Pa-s/m\({}^{2}\)} & 854 Hz & 41.88 dB \\  & 1467 Hz & 18.85 dB \\  & 1588 Hz & 43.61 dB \\ \hline \multirow{3}{*}{104,400 Pa-s/m\({}^{2}\)} & 854 Hz & 40.43 dB \\  & 1467 Hz & 17.75 dB \\  & 1588 Hz & 42.41 dB \\ \hline \multirow{3}{*}{69,600 Pa-s/m\({}^{2}\)} & 854 Hz & 39.27 dB \\  & 1467 Hz & 16.82 dB \\  & 1588 Hz & 41.32 dB \\ \hline \multirow{3}{*}{0.97} & 854 Hz & 40.63 dB \\  & 1467 Hz & 17.80 dB \\  & 1588 Hz & 42.50 dB \\ \hline \multirow{3}{*}{0.99} & 854 Hz & 40.73 dB \\  & 1467 Hz & 17.81 dB \\  & 1588 Hz & 42.53 dB \\ \hline \multirow{3}{*}{0.95} & 854 Hz & 40.54 dB \\  & 1467 Hz & 17.79 dB \\  & 1588 Hz & 42.46 dB \\ \hline \multirow{3}{*}{2.52} & 854 Hz & 39.22 dB \\  & 1467 Hz & 17.86 dB \\  & 1588 Hz & 17.86 dB \\  & 1588 Hz & 43.17 dB \\ \hline \multirow{3}{*}{5.04} & 854 Hz & 40.44 dB \\  & 1467 Hz & 17.78 dB \\  & 1588 Hz & 42.42 dB \\ \hline \multirow{3}{*}{1.26} & 854 Hz & 41.68 dB \\  & 1467 Hz & 16.06 dB \\ \cline{1-1}  & 1588 Hz & 39.51 dB \\ \hline \end{tabular}
\end{table}
Table 4: Table of radiated sound power level results for foam-filled panels at various static flow resistivity, porosities, and tortuosity factors.  
In conclusion, an increase in porosity results in a gradual decrease in radiated sound power at various peak points. Nonetheless, within an acceptable range and without accounting for density changes attributable to porosity fluctuations, the impact of porosity on the radiated sound power is relatively insignificant.