# Acoustic Applications of a Foamed Geopolymeric-Architected Metamaterial
## 2 Materials and Methods
### Methods
#### Acoustic Characterization  
This study investigated the material's static airflow resistivity (SAR) under ISO 9053:1991 [72]. Airflow resistivity measures how easily air can pass through a material, which is a critical parameter in determining the sound absorption properties of a porous material. An alternating air flow method was adopted [73]. This method is recognised for its simplicity, accuracy, and ability to measure resistivity over various airflow velocities [73; 74]. The setup employed a specially designed device comprising a cylindrical tube, a piston system with a rotating cam for generating alternating airflow, and a pressure microphone for measuring the pressure fluctuations within the tube (Figure 5a). The measurements were repeated with different cams to assess their impact on the airflow resistivity of the tested material [73]. The alternating air flow method has several advantages over other methods, including:  
* It requires a smaller sample size than the impedance tube method. This is because the sound field is more uniform around the sample, reducing the edge effects. * It can measure airflow resistivity over a broader range of airflow velocities than other methods. This is because the geometry of the impedance tube does not restrict the airflow. * It is faster than other methods. This is because the measurement does not require a frequency sweep. The alternating air flow method is a powerful tool for measuring airflow resistivity. It is particularly well-suited for measuring SAR of materials with high airflow resistivity or for measuring SAR over a wide range of airflow velocities. The sound absorption coefficient (SAC) measurements were carried out under ISO-10534-2:1998 [75]. Sound absorption coefficient measurements play a crucial role in understanding the acoustic properties of materials [76]. Accurate and reliable measurements are essential for designing spaces with optimal acoustic conditions. One widely accepted method for determining sound absorption coefficients is the impedance tube, which has proven effective in various applications using perforated panels [77; 78]. This is the case of our samples consisting of perforated geopolymeric ceramic foams. Sound absorption refers to the process by which sound energy is absorbed by a material rather than being reflected. The sound absorption coefficient quantifies this behaviour and is defined as the ratio of absorbed sound to incident sound energy. The impedance tube (or Kundt tube) is the classic apparatus used for measuring the speed of sound in gases and determining the acoustic properties of materials, including sound absorption coefficients. The device consists of a long, narrow tube filled with the material under investigation (Figure 5b). A sound source generates standing soundwave at one side while a movable piston at the opposite side of the tube varies its length until resonance occurs. The impedance tube used in our tests is the Model SCS type 9020B/K operating on the principle of tested material natural resonance frequency. Namely, the standing wave within the tube sets up high- and low-pressure areas, causing the material to vibrate at the same frequency as the sound wave. By adjusting the tube's length until resonance is achieved, we can determine the wavelength of the sound wave. This infor  
Figure 5: (**a**) Airflow resistance measurements instrument. (**b**) Impedance tube for measuring the absorption coefficient at normal incidence (Model SCS type 9020B/K). mation, along with the frequency of the sound source, allows for calculating the speed of sound in the material. The sound absorption coefficient (SAC) can be deduced from the sound speed and the material's density [75]. This study used an impedance tube with the following dimensions: an internal diameter of 10 cm (corresponding to an upper-frequency limit of 2000 Hz), a length of 56 cm, and two \(14\arcsec\) microphones placed at 5 cm for measurements above 200 Hz. These dimensions were selected to ensure accurate and reliable measurements across various frequencies.