# Acoustic Applications of a Foamed Geopolymeric-Architected Metamaterial
## 3 Results and Discussion
### Sound Absorption Coefficient Results
This shift in performance at lower frequencies for the thicker sample suggests that the acoustic behaviour is more sensitive to thickness variations in this frequency range. The observed trends in Figure 11b can be justified by considering the interplay between mass, thickness, and perforations, which collectively influence the acoustic absorption characteristics of the material across different frequency ranges. Figure 11c compares the single-layer sample with a thickness of 20 mm and a full 40 mm and the double sample with a full thickness of 60 mm. We can see that the solid double sample at 60 mm thickness returns higher values in the frequency range from 250 Hz to 2000 Hz. For the single-layer samples, we see that at frequencies from 160 to 500, the 40 mm thickness sample returns higher than the sac, while at higher frequencies, it is the one at 20 mm, which returns higher values. The observed trends are in Figure 11c, comparing the single-layer samples with thicknesses of 20 mm and 40 mm, along with the double sample with a total thickness of 60 mm, which can be justified by considering the interplay of thickness and configuration on acoustic absorption characteristics. For the solid double sample with a thickness of 60 mm, higher values in the frequency range from 250 Hz to 2000 Hz are likely attributed to the combined effect of increased mass of negative stiffness metamaterial and its thickness. The additional thickness contributes to enhanced low- and mid-frequency absorption capabilities, while the increased mass further aids in the dissipation of sound energy across the specified frequency range. The synergy of these factors results in the solid double sample exhibiting higher sound absorption coefficient (SAC) values within this frequency band. When comparing the single-layer samples, the 40 mm thick sample returns higher values than the SAC in the frequency range from 160 Hz to 500 Hz. This can be attributed to the increased mass and thickness, which contribute to improved low-frequency absorption. In contrast, the 20 mm thick sample returns higher values at higher frequencies. This shift in performance is likely due to the thinner sample  
being more responsive to higher frequencies, where the mass and thickness are not as critical, and other acoustic mechanisms, such as perforations or resonance, might play a more significant role. The observed trends in Figure 11c emphasise the importance of considering both thickness and configuration in the context of acoustic absorption. The thickness of the material influences its performance across different frequency ranges, with the combination of increased negative stiffness metamaterial mass and thickness generally contributing to improved absorption capabilities, especially in the low- to mid-frequency range. The specific configuration, such as the presence of perforations or the arrangement of layers, further modulates the acoustic behaviour, leading to the observed variations in SAC values across the frequency spectrum. Figure 11d compares the solid and perforated double-layer samples with a thickness of 60 mm for a length of 20 mm. We can see that the drilled samples have a higher SAC in the frequency range from 400 Hz to 1600 Hz compared to the double solid one at 60 mm. The trends observed in Figure 11d, where the solid and perforated double-layer samples with a thickness of 60 mm and a length of 20 mm are compared, can be explained by the impact of perforations on the acoustic absorption characteristics within specific frequency ranges. The frequency ranges from 400 Hz to 1600 Hz, and the perforated double-layer samples exhibit higher sound absorption coefficient (SAC) values than the double solid sample at 60 mm thickness. This phenomenon is likely attributed to drilled perforations, which introduce additional mechanisms for sound absorption.