# Acoustic Applications of a Foamed Geopolymeric-Architected Metamaterial
## 3 Results and Discussion
### Sound Absorption Coefficient Results  
In this study, different samples of the foamed geopolymer were used, and to increase the sound absorption properties, these samples were assembled to simulate a Helmholtz resonator [84]. Helmholtz resonators consist of a cavity connected to the environment by a small opening called the resonator neck, which is typically much smaller than the cavity. When a sound wave strikes the inlet of the resonator, the air in the neck oscillates, much like an oscillating piston [85]. At the same time, the air inside the cavity is alternately compressed and expanded, acting like a spring. Resonators exhibit heightened absorption at their resonant frequency but minimal absorption at other frequencies. Consequently, it becomes feasible to construct precisely  
Figure 8: Frequency sweep viscoelastic response of the foamed hybrid geopolymer in the dynamic mechanical tester operating at 25 \({}^{\circ}\)C and in the range of frequencies from \(10^{-3}\) to \(10^{3}\) Hz. calibrated devices for absorbing specific frequencies. To simulate the behaviour of the Helmholtz resonator, two samples of different thicknesses (40 mm and 60 mm) were used with perforations of various thicknesses and lengths. Eight different combinations of samples were assembled to measure performance as a sound-absorbing material (Table 3 and Figure 9). Initially, our investigation involved the measurement of static flow resistance, a parameter assessed under the guidelines stipulated in ISO 9053:1991 [72]. Multiple measurements were conducted on various samples, each constructed by positioning the bulk material within a 20 mm thick support. The acquired measurements were subsequently averaged to derive representative values for analysis. We measured a static flow resistance of 27.000 Rayl/m. Figure 10 illustrates the sound absorption coefficient values measured at normal incidence, plotted against frequency. The data represents each of the eight sample types listed in Table 3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample Layout** & **Thickness (mm)** & **Sample Type** & **Hole Thickness** & **Hole Diameter** \\  & & & **(mm)** & **(mm)** \\ \hline Single & 20 & full & - & - \\ Single & 20 & drilled & 20 & 7 \\ Single & 40 & full & - & - \\ Single & 40 & drilled & 20 & 7 \\ Double & 20,40 & full & - & - \\ Double & 20,40 & drilled & 20,20 & 7 \\ Double & 20,40 & drilled & 20,20 & 9 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Properties of different combinations of samples. Figure 9: Samples of different thicknesses and perforation design. Upon conducting an initial analysis of the sound absorption coefficient trends, a notable observation emerges, indicating that the configuration involving double specimens featuring perforations to simulate the characteristics of a resonator yields the most favourable outcomes [86]. Specifically, the curves associated with the doubled specimens exhibit elevated sound absorption coefficient (SAC) values, particularly within 250 Hz to 1250 Hz. This suggests that including double specimens with perforations significantly enhances the absorption capabilities in the specified frequency spectrum. The distinct advantage becomes evident as these configurations outperform others in effectively attenuating sound across the analysed frequencies. In Table 4 we compared the measured values of the sound absorption coefficient of the metamaterials under investigation in this study with those already available in the literature of two of the most common synthetic materials (fiberglass and sprayed cellulose fibre). 125 & 0.22 & 0.14 & 0.14 & 0.18 & 0.13 & 0.13 & 0.19 & 0.21 & 0.06 & 0.08 \\
250 & 0.22 & 0.10 & 0.30 & 0.21 & 0.41 & 0.32 & 0.28 & 0.28 & 0.2 & 0.29 \\
500 & 0.17 & 0.15 & 0.38 & 0.35 & 0.50 & 0.81 & 0.74 & 0.64 & 0.65 & 0.75 \\
1000 & 0.31 & 0.39 & 0.22 & 0.39 &From the comparison, we can verify that the SAC of the materials studied are comparable with those of the materials already available in the literature [87], or even better as is the case at 125 Hz.