## 1 Introduction
The frequency working range can be tuned, adjusting the weight of the masses, if present, or other constructive parameters to place the resonant effect even in the low frequency range. Stacking more than one metamaterial panel together can be a strategy to obtain a more broadband effect. Another type of singular negative metamaterial can be obtained when the effective bulk modulus turns negative. In [PERSON] et al. [18], inspired by results obtained in the electromagnetic field, an array of sub-wavelength Helmholtz resonators is used to obtain this effect in the ultrasonic regime. Dipolar and monopolar local resonances were proved to be the essential wave mechanisms for producing, respectively, a negative effective mass density and a negative effective bulk modulus of the metamaterial. Double negative acoustic metamaterials can be achieved by combining negative density and negative compressibility materials, or by overlapping monopolar and dipolar resonances in the same frequency range, or to design phononic crystals to generate a band folding through multiple scattering in a periodic structure. Different and more complex devices with equivalent dynamic or electromagnetic lumped models have been developed so far [19] to obtain metamaterials, based on locally resonant elements that show single or double negativity, depending on the considered frequency working range [19; 20; 21]. Other approaches have also been successfully adopted to realize metamaterials with interesting properties, such as coiling up space by using labyrinthine structures to introduce local phase delay in sound propagation. The phase shift can be designed in the full 0-2\(\pi\) range to obtain flat surfaces to act as arbitrarily-shaped virtual surfaces [22; 23; 24], modifying the reflection angle, or it could be random to maximize acoustic diffusion [25; 26] (Figure 1). Space-coiling metamaterials can be adopted to obtain lens-like behaviors or even to transform the propagation pattern from spherical to plane waves [27; 28]. Furthermore, this approach allows for an effective dynamic \(\rho<0\) and \(\mathcal{K}<0\), and hence, a negative refractive index to be obtained in the deep sub-wavelength regime with a quite simple device [29; 30]. When a metamaterial device is built with a thickness below a tenth of the working wavelength, it is commonly called a metasurface. There is obviously a great interest in developing metasurfaces, as a reduced thickness is often desirable for real applications. Coiled-up space devices and resonant membranes were intrinsically designed to lead to metasurfaces, and hence, the majority of the so-based work presented in previous paragraphs classifies as metasurfaces, due to their deep sub-wavelength thickness. However, for each of the approaches presented above, some engineered metasurfaces can be found in the literature [31; 32; 33; 34; 35]. A very interesting superabsorber with micro-bubble insertions was presented in [36]. A significant sub-wavelength attenuation of sound was shown due to the resonance of the bubbles in a soft elastic matrix, breaking the mass density law (which states that the amplitude of transmittance for a solid panel is proportional to the inverse of the product of the density and the thickness of the panel and the frequency of the acoustic perturbation). Thermo-viscous losses at the solid-fluid interfaces inside metamaterial components are crucial in determining the behavior of metamaterials. This is particularly true for concepts that consider micro-slits, micro-cavities and/or narrow channels as part of the design, like space-coiling metamaterials. The visco-thermal loss mechanism becomes non-negligible even when the widths of the slits are about two order of magnitude bigger than the viscous and thermal boundary layers (in the order of \(10^{-5}\) m) and is enhanced by the fact that high amplitude standing waves can form in small cavities.