## 3 Methods  
The review presented in the previous section shows that, even if a limited number of papers investigated the EoLHM acoustic performances, these materials have exploitable properties for the improvement of the indoor acoustic quality. An ideal panel suitable to be used as a facade element posses both good sound absorption and high transmission loss. As concerns the transmission loss, it must be remembered that the final acoustic performance will also depend on the basic wall on which they will be installed. In this study, the acoustic properties of different panels, realized by coupling different EoLHM, are experimentally investigated to understand whether further studies are required. Tests have been performed on samples made of easily obtainable CoLHM such as cardboard, textile waste, egg-boxes, metallic elements and their combination. Since the acoustic conditions of the environment in which these panels will be installed are unknown, configurations with high sound absorption coefficient and good \(TL\) are considered interesting and worth to be further investigated. Since this analysis is exploratory, the experimental tests have been performed by means of the impedance tube method that requires small samples and gives reproducible results. However, this technique allows the determination of the properties for sound waves impinging normally on the sample surface. The experimental investigation of the acoustic properties was performed following the standard procedure given by the ASTM E2611 [55] that required the use of a four-microphone impedance tube (Figures 5 and 6). This device consists of two tubes of equal internal cross section connected to a test sample holder. Four microphones were placed along the tube (two on either side of the specimen). A source emitting a pink noise was placed at one end of the tube. A multi-channel Fast Fourier Transform (FFT) analyzer acquired the signals captured by the microphones. The second endpoint of the tube could be equipped with an anechoic or a reflecting termination, allowing us to perform the tests with two different boundary conditions. The pressure and particle velocity of the traveling waves and of reflected waves could be determined by means of a MATLAB script implemented on the basis of the E2611 ASTM standard [55]. The frequency range investigated went from 100 Hz to 3150 Hz. Defining the wave number in air, \(k=2\pi\cdot f/c_{0}\), the traveling and reflected components of the plane wave propagation in the tube (A, B, C and D) can be calculated using the following correlations, once the complex acoustic transfer functions \(H_{i,ref}\) between the \(i\)th microphone and the reference microphone are measured:  
\[A=0.5\times j(H_{1,ref}e^{-jkL_{1}}-H_{2,ref}e^{-jk(L_{1}+s_{1})}/sin(ks_{1}) \tag{18}\]  
Figure 5: Schematic drawings of a four-microphones impedance tube. \(A\) represents the energy emitted by the loudspeaker, \(C\) is the component that crosses the sample, \(D\) is the component reflected by the termination, and \(B\) is the component reflected by the sample and/or that crosses the sample after being reflected by the termination. Figure 6: Impedance tube used for the determination of the acoustic properties of CoLHM. \[B =0.5\times j(H_{2,ref}e^{+jk(L_{1}+s_{1})}-H_{1,ref}e^{+jk(L_{1})})/sin( ks_{1}) \tag{19}\] \[C =0.5\times j(H_{3,ref}e^{+jk(L_{2}+s_{2})}-H_{4,ref}e^{-jk(L_{2})})/ sin(ks_{2})\] (20) \[D =0.5\times j(H_{4,ref}e^{-jkL_{2}}-H_{3,ref}e^{-jk(L_{2}+s_{2})})/ sin(ks_{2}) \tag{21}\]  
where, in the case at hand, microphone 1 was selected as the reference microphone. For a given boundary condition, it is possible to determine the acoustic pressure \(p\) and the particle velocity \(u\) on each face of the specimen using the following equations:  
\[p_{0}=A+B\hskip 28.452756 ptp_{d}=Ce^{-jkd}+De^{+jkd} \tag{22}\]  
\[u_{0}=\frac{A-B}{\rho_{0}c_{0}}\hskip 28.452756 ptu_{d}=(Ce^{-jkd}-De^{+jkd})/ \rho_{0}c_{0} \tag{23}\]  
where \(\rho_{0}\) is the density of air.