# Acoustic Applications of a Foamed Geopolymeric-Architected Metamaterial
## 3 Results and Discussion
### Sound Absorption Coefficient Results
To better understand the behaviour of the different types of combinations, we compare them by groups. Figure 11 compares the solid and perforated length of a single-layer sample with a thickness of 20 mm. We can see that the solid sample returns slightly higher values in the frequency range from 160 Hz to 800 Hz. For higher frequencies, the perforated sample returns higher values than the SAC. The observed variations between the solid and perforated single-layer samples, both having a thickness of 20 mm along the entire length, can be justified by the distinct acoustic characteristics of the materials at different frequency ranges. The solid sample exhibits slightly higher values from 160 Hz to 800 Hz in the frequency range. A possible explanation for this behaviour could be related to the negative stiffness and highly dissipative characteristics of the foamed geopolymeric samples occurring at frequencies above 100 Hz (see DMA tests of Figure 8) that are magnified by the additional resonance effects introduced by perforations. At higher frequencies, the perforated sample surpasses the solid sample, reaching higher sound absorption coefficient values (SAC) values. Figure 11: Sound absorption coefficient for foamed geopolymer samples: (**a**) Single-layer samples full and drilled (thickness: 20 mm); (**b**) Single-layer samples full and drilled (thickness: 40 mm); (**c**) Single- and double-layer samples full (thickness: 20 mm, 40 mm, 60 mm); (**d**) Double-layer samples full and drilled with different configurations. This trend can be elucidated by the perforations' capacity [77; 78] to introduce acoustic impedance mismatches, leading to increased sound absorption efficiency at higher frequencies. The perforations likely contribute to dissipating sound energy effectively in this frequency range, demonstrating their advantage over the solid counterpart [85; 86]. Therefore, the observed variations in sound absorption performance between the solid and perforated samples can be rationalised by considering the specific frequency-dependent characteristics of the foamed material (behaving as a negative stiffness metamaterial) and the unique acoustic mechanisms associated with each perforation configuration of the samples [77; 78]. Figure 11a compares the single-layer sample with a thickness of 40 mm, solid and perforated for the entire length. We can see that the solid sample returns higher values in the frequency range from 160 Hz to 500 Hz. As described before, the perforated sample returns higher SAC values at higher frequencies, even in this case. Compared with Figure 11, we can see that the sample with greater mass slightly increases the acoustic absorption coefficient at low frequencies. While the sample with greater thickness at higher frequencies presents lower values. It is also noted that the change in performance occurs at lower frequencies for the sample with greater thickness. The differences observed in Figure 11b between the solid and perforated single-layer samples, with a thickness of 40 mm along the entire length, can be explained by considering the impact of the higher mass of the negative stiffness high dissipative foamed geopolymer on acoustic absorption across the specific frequency range highlighted by the dynamic mechanical analysis (Figure 8). Conversely, at higher frequencies, the perforated sample exhibits higher SAC values. The perforations in the material introduce mechanisms such as Helmholtz resonance and greater surface area, enhancing its ability to absorb sound energy at higher frequencies. This phenomenon aligns with the perforated sample's advantage in dissipating sound energy efficiently in the higher frequency range. When comparing Figure 11b with Figure 11a, the influence of thickness becomes apparent. The sample with a greater thickness (40 mm) exhibits a slight increase in acoustic absorption coefficient at low frequencies compared to the 20 mm thick sample. However, at higher frequencies, the thicker sample presents lower SAC values.