# Cross-Laminated Timber Floor: Analysis of the Acoustic Properties and Radiation Efficiency
## 2 Materials and Methods
### Acoustic and Vibration Parameters Determined from Measurements  
The normalized impact sound pressure level, \(L_{\mathrm{n}}\), measured with a standard tapping machine and the energy average maximum impact sound pressure level measured with rubber ball, \(L_{\mathrm{i,Fmax}}\), are determined according to ISO 10140-3 [46]. Weighted indices, \(L_{\mathrm{n,w}}\), evaluated from 100 Hz to 3150 Hz, and \(L_{\mathrm{i,Fmax}}\), evaluated from 50 Hz to 630 Hz, have been derived according to ISO 717-2 standard [61]. For the measurements with the tapping machine and with the rubber ball, 4 positions of the source (A, B, C, D) and 5 fixed positions of the microphone (R1, R2, R3, R4, R5) have been used as depicted in Figure 4. \begin{table}
\begin{tabular}{c c c c} \hline \(E_{\mathrm{m,0,mean}}\) & \(E_{\mathrm{m,90,mean}}\) & \(\rho_{\mathrm{mean}}\) & \(m^{\prime}\) \\ \hline
11 kN/mm\({}^{2}\) & 0.37 kN/mm\({}^{2}\) & 420 kg/m\({}^{3}\) & 84 kg/m\({}^{2}\) \\ \hline \end{tabular}
\end{table} 
Table 1: Mechanical properties of the CLT under consideration. Figure 3: Airborne noise source (**a**), tapping machine (**b**) and rubber ball (**c**). The sound reduction index, \(R\), is calculated according to ISO 10140-2 [45]. The weighted sound reduction index, \(R_{\rm w}\), is evaluated in the frequency range 100-3150 Hz and is calculated according to ISO 717-1 [62]. For the measurement of the sound reduction index two positions (A, C) of the source and 5 positions of the microphone have been used (Figure 4). For all the measurements, the microphones have been positioned in a range of heights between 1 and 1.5 metres in order to avoid positions on the same plane. Velocity levels were measured with an accelerometer fixed in 9 positions with screws. A reference velocity value, \(v_{0}\), of \(10^{-9}\) m/s has been considered. The noise sources (tapping machine, dodecahedron and rubber ball) were positioned at 3 points (A, B, C) for a total of 27 measurements, according to ISO 10848-1 [63] (Figure 5). Radiation power, \(W_{\rm rad}\), radiation efficiency, \(\sigma_{rad}\) and radiation index, \(L_{\sigma_{rad}}\), are derived by the Equations (1)-(3) [64]:  
\[W_{rad}=A\frac{\langle p^{2}\rangle_{S,t}}{4\rho_{0}c_{0}}\bigg{(}1+\frac{S_{T }\lambda_{0}}{8V}\bigg{)}, \tag{1}\]  
\[\sigma_{rad}=\frac{W_{rad}}{S(v^{2})_{S,t}\rho_{0}c_{0}} \tag{2}\]  
\[L_{\sigma_{rad}}=10\lg(\sigma_{rad}) \tag{3}\]  
where \(A\) is the equivalent absorption area of the receiving room, \(\langle p^{2}\rangle_{S,t}\), is the average sound pressure (with tapping machine, dodecahedron or rubber ball), \(\rho_{0}\) is the air density, \(c_{0}\) is the speed of sound, \(S_{\rm T}\) is the room surface, \(\lambda_{0}\) is the wavelength and \(V\) is the room  
Figure 4: CLT floor and sources positions (**a**); microphone positions in the transmitting room (**b**) and in the receiving room (**c**). Figure 5: General scheme of the positioning of the sound sources (**a**) and the accelerometer (**b**) for the determination of the velocity levels. volume, \(S\) is the floor surface and \(\left\langle v^{2}\right\rangle_{S,t}\) is the average square vibration velocity (with tapping machine, dodecahedron or rubber ball).