# Resonant Acoustic Metamaterials
## 3 Research Methodology: Resonant System Configurations and Test Conditions  
The scope of this paper is the study of a different type of scatterers used to improve acoustic absorption, including 2D scatterers and 2D scatterer resonators [28; 29]. Two-dimensional scatterer resonators refer to a system composed of empty cylinders equipped with a series of holes on the external surface (resonators) that connect the cavity to the exterior, which are constantly re-distributed [30]. Applications of this type of resonant scatterers can be represented by the creation of acoustic filters for the noise attenuation of fans in cooling systems and for the attenuation of road traffic noise [31]. In this paper, acoustic measurements were conducted inside a semi-anechoic chamber of 4.4 \(\times\) 4.4 \(\times\) 4.5 m, characterized with absorption on the walls and ceiling, and concrete-finish flooring. Figure 4 shows the equipment employed during the acoustic measurements, with the set-up scheme created for the performance of _IL_ measurements [32]. Figure 3: Scale model of metamaterial acoustic barrier. Figure 2: Soundwave propagation scheme when an incident wave impacts against a regular geometric structure. The loudspeaker was fed a pink noise equalized over all the frequency bandwidth [33] and placed in a box whose surfaces were coated with absorbing mats to stop any potential standing waves. This box has an openable lid at the top, where the metamaterial acoustic element was installed. An omnidirectional microphone was installed at 1 m from the test sample. The acoustic tests were carried out with the following two specific configurations to calculate the _IL_:  
* Sound-pressure-level difference measured without samples. * Sound-pressure-level difference measured with the test samples. A smaller box was built to better assess the _IL_ attenuation of the noise that was generated by the loudspeaker and passed through the test sample. The dimensions of the box were 1.2 \(\times\) 1.3 \(\times\) 0.5 m.  
The implementation of this measurement scheme allowed the computation of the attenuation to only involve the function of the interference given by the scatterers [34], excluding the diffraction effects of the edges. The acoustic measurements were out on the following test samples:  
* Smooth wooden scatterers of 15 mm diameter with the addition of a plastic empty scatterer of 20 mm diameter with a 1.5 mm thickness. * Five holes of 5 mm diameter were created on the external surface of the plastic empty scatterers. The length of the bar is always kept constant, equal to 300 mm for all tests, as shown in Figure 5.  
The samples were tested individually based on the following configurations:  
* Configuration A1, composed of 1 row of wooden scatterers with a 15 mm diameter. * Configuration A2, composed of 2 rows of wooden scatterers of 15 mm diameter, with a distance between the rows equal to 15 mm. * Configuration A3, composed of 3 rows of wooden scatterers of 15 mm diameter, with a distance between rows equal to 15 mm. * Configuration A4, composed of 4 rows of wooden scatterers of 15 mm diameter, with a distance between rows equal to 15 mm. * Configuration B1, composed of 1 row of empty scatterers of 20 mm diameter. * Configuration B2, composed of 2 rows of empty scatterers of 20 mm diameter, with a distance between rows equal to 20 mm. * Configuration B3, composed of 3 rows of empty scatterers of 20 mm diameter, with a distance between rows equal to 20 mm. Figure 4: Equipment scheme during the acoustic measurements (**left**). View of the laboratory during the measuring tests (**right**). * Configuration B4, composed of 4 rows of empty scatterers of 20 mm diameter, with a distance between rows equal to 20 mm. * Configuration C1, composed of 1 row of perforated empty scatterers of 20 mm diameter and 1 row of empty scatterers of 20 mm diameter, with a distance between rows equal to 20 mm.