## 1 Introduction  
Metamaterials are artificial materials composed of periodic cellular structures not existing in nature [1]. This innovation represents a new benchmark in the field of applied acoustics, since the control of the sound propagation is strictly dependent on the interaction between the incident sound waves and the geometry of the external surface [2]. The presence of modular elements composing the periodic structures is favorable in creating such sound attenuation through the destructive interference of the sound waves when the latest ones penetrate the gaps of the whole structure [3]. The scattering effects generated by regular and periodic geometries were initially studied in the field of electromagnetism. This concept follows the regime of [PERSON]'s law, such that the band gap frequency (\(f_{BG}\)) depends on the incident angle of the wave (\(\phi\)), the lattice constant (\(\alpha\)), and the sound speed in the medium (\(c\)) [4], as summarized in Equation (1). \[f_{BG}=\frac{c}{2\alpha\ \sin(\phi)} \tag{1}\]  
On this basis, when a plane wave affects a structure composed of elements arranged with a regular geometry, the distance between the wavefronts can be described as \(a\ \sin(\phi)\), where (\(\phi\)) is the angle of incidence of the plane wave, \(a\) is the distance between two consecutive rows of scatterers, and \(\lambda\) is the wavelength of the incident wave. The condition for the destructive interference is that \(\lambda/2=a\sin\left(\phi\right)\). At normal incidence, this implies that the stop band or the Bragg's pass band frequency is equal to \(f_{BG}=\frac{c}{2a}\). Figure 1 shows the scattering of a plane sound wave when hitting a barrier composed of two rows of scatterers. By applying these theories to acoustics, development of the sonic crystals took place, since the metamaterials are considered solid materials, subject to interaction with a dynamic fluid (i.e., air, water). Under these conditions, sound attenuation can be achieved at any frequency, despite some traditional sound-absorbing materials that are not suitable for this scope [5,6]. According to [PERSON] and [PERSON] [7], specific physical properties related to the elastic modulus, mass density, and refractive index occur to create the destructive interference and hence the band gap. The IL is strictly related to the density of the material used for the scatterers, to the ratio of the volume occupied by the scatterers in a determined volume of the crystal that is called the filling factor (_ff_), and to the lattice design, which can assume different shapes [8]. Generally, the band gap attenuation that is aimed to be achieved for road traffic noise, characterized by a medium frequency wavelength, depends on the cylinder's radius rather than on the space between scatterers, while the amplitude of attenuation depends on the filling factor [9]. To obtain an effective frequency-selection attenuation, the modularity or the periodicity of the scatterers' arrangement shall be in place along with the distance between source and barrier. The baseline principle of creating an acoustic barrier, composed of a certain number of cylindrical scatterers periodically installed, represents the phenomenon of diffraction that redirects the streaming of the soundwaves across the voids, as shown in Figure 2.  
This technique has also been used by artists (e.g., [PERSON]), who arranged the installation of artworks based on specific characteristics, listed as follows:  
* Selection of a geometric shape for the scatterers' configuration,
* Determination of the distance between elements,
* Height of the modular scatterers (constant/irregular),
* Selection of scatterers' diameter. The periodic-structure artworks represent a source of inspiration for sound crystal research, which tries to reduce or mitigate road traffic noise pollution in accordance with the divergence phenomenon.