## 1 Introduction
Table 1 presents measurements of pore-structure information used to determine how the sound absorption spectra for these materials can be numerically derived (to be discussed later). \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Samples**} & \multirow{2}{*}{**ALF [3]**} & **PCF** & **NCX2733** & \multirow{2}{*}{**SFM [6]**} & **GWF [7]** & **A/DL1 [8]** \\  & & & [14; 15; 16] & & & \\ \hline Measurements & & & & & & \\ Foam thickness (mm) & 20.00 & 16.50 & 10.00 & 23.31 & 25.00 & 40.00 \\ Foam porosity & 60.00 & 87.92 & 89.93 & 90.94 & 98.70 & 70.54 \\ Static viscous tortuosity & 1.87 & 1.27 & 1.15 & 1.51 & 1.01 & 1.71 \\ Viscous characteristics length (\(\upmu\)m) & 155.00 & 97.60 & 308.69 & 112.99 & 132.00 & 96.25 \\ Thermal characteristics length (\(\upmu\)m) & 800.00 & 190.20 & 343.71 & 193.78 & 237.00 & 302.88 \\ Darcian permeability/\(10^{-9}\)(m\({}^{2}\)) & 0.81 & 0.75 & 2.85 & 0.96 & 1.08 & 0.48 \\ Airflow resistivity (Pa.s/m\({}^{2}\)) & 22,475.31 & 24,436.24 & 6377.20 & 18,980.00 & 16,800.00 & 37,927.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Tabular representation of measured pore-structure-related information for several soundproofing materials. A substantial amount of literature exists containing empirical, phenomenological, and semi-phenomenological models of soundproofing materials' acoustical properties. For example, [PERSON] and [PERSON] [19] proposed equivalent fluid models to describe the vibroacoustic behaviour of elastic porous materials and have been in use for many decades. The coupling coefficients of the models in [19] were improved in order to better approximate pressure waves inside cellular matrices [20]. Other predictive models [21; 22; 23; 24; 25; 26; 27; 28] have been developed for describing the sound absorption properties of soundproofing devices based on pore structure ranging from being transversely isotropic (high porosity [21; 22]) to having cylindrical pores and cavities (low porosity [19]). Figure 1 shows the numerical  
Figure 1: Above the plots of normal and numerically simulated normal incidence sound absorption coefficient, Ac [–] against resonant frequency are images of several soundproofing materials: (**a**) porous aluminium foam (ALF) [3], (**b**) polyhedral ceramic foam (PCF) [14; 15; 16], (**c**) nickel-chrome extra-strong NCX2733 [13], (**d**) sintered fibre metal (SFM) [6], (**e**) glass wool fibre (GWF) [7] and (**f**) bimodal aluminium foam (BAF) [18]. applicability of these models to successfully predict experimental data on sound absorption spectra for several soundproofing materials (images in Figure 1), whose pore volume fractions range between 0.60 and 0.98, as shown in Table 1. The simulations in [14; 29; 30] show the Wilson relaxation-matched model proposed in [27] has a good fit and fully overlaps absorption spectra for bottleneck-shaped aluminium (ALF) [14; 30] and polyhedral ceramic foams (PCF) [9; 14]. A key reason for the accuracy is that the Wilson model was developed to predict the transition in relaxation behaviour for boundary layers in structures characterised by near-circular pores, which closely resemble \"bottleneck-shaped\" materials [14; 29]. Furthermore, the acoustic properties of the high porosity (\(\epsilon\)\(\sim\)0.909) sintered fibre metal (SFM) were successfully predicted in [8; 9] by numerically simulating the semi-phenomenological Johnson-Champoux-Allard (JCA) model [24], indicating a better prediction of the sound absorption spectrum for Recemat NCX 2733 sample, as illustrated in Figure 1. This further increases the ability of JCA's model to predict the acoustic properties of structures with non-uniform pores and constrictions [17]. Additionally, Figure 1 exhibits a striking overlap between numerical simulations using the Delany-Bazley-Mikki (DBM) poro-acoustic model [23] and the measured data for glass wool fibrous (GWF) material described in [8].