## 3 Methods
### Measurement of Sonic Velocity
#### 3.2.2 Experimental  
The boards were tested to acquire the velocity of a longitudinal sonic wave that propagates in the board from one end to the other. The instrumentation used consists of the following system (Figure 2):  
* an impact hammer with piezoceramic sensor for generating the signal,
* a piezoelectric transducer for receiving the signal,
* a Velleman Instruments digital oscilloscope for signal visualization and preliminary analysis, and
* a PC for data storage and signal processing. In order to reduce the dissipation of the signal caused by the difference in acoustic impedance of the two materials in contact, a layer of mastic was applied to the surface of the receiver in contact with the board and used as coupling agent. The test schematic is shown in Figure 3.  
The test detects the time t taken by the wave impressed by the hammer at one end of the board to reach the receiver transducer placed at the other end. Known the length 1 of the table, assumed as the space travelled by the wave, the propagation velocity is obtained as  
\[\text{V}=\text{1/t}. \tag{6}\]  
Note that V represents an apparent velocity, as it is calculated as a function of the distance 1 between the emitter and the receiver and not as a function of the real, unknown path that the wave travels inside the material. This approximation is widely accepted in the context of sonic and ultrasonic non-destructive testing. For each board, the measurement was repeated three times and the average of the results was considered. Figure 2: Instrumental set. Density and velocity have an inverse relationship with moisture content with respect to each other. As the drying progresses and the moisture level decreases, a decrease in density is observed, as expected, resulting from the decrease in the water content inside the wood. On the contrary, the decrease in moisture content corresponds to an increase in the propagation velocity of the sonic wave, in accordance with the existing literature [61; 62; 63] on the relationship between wave velocity and moisture content, which presents different relationships depending on of the wood species. In most species, the increase in velocity from the wet state to the saturation point is not very significant, while from the saturation point to the dry state it is much greater; this is explained as follows [52]. For low water contents (U < 18%), when water is present in the cell walls as bound water, the elastic wave is dispersed by the wood and the cell boundaries. The lateral units of OH or other radicals of the cellulosic material can reorient their position under the elastic stress. In this case, the attenuation mechanism related to the cellulosic cell wall material is probably the most important. With a higher moisture content but below the saturation point, scattering at the cell boundaries may be the most important loss mechanism. When the saturation point is exceeded and free water is present in the cell cavities, the porosity of the material takes over as a predominant factor in the dispersion of the elastic wave. Starting from equation 5, the MoEdyn value in the wet and dry conditions was calculated obtaining the average values shown in Table 3.  
In the transition from the wet to the dry condition, an increase in the average MoEdyn of about 8% is observed. Figure 6 shows the variation of MoEdyn with moisture content; an almost non-significant correlation is observed. Figure 5: Velocity V as a function of moisture content U. \begin{table}
\begin{tabular}{c c c} \hline  & **U [\%]** & **MoEdyn [N/mm\({}^{2}\)]** \\ \hline
**wet** & \(22.5\pm 5.0\) & \(7743\pm 1595\) \\
**dry** & \(11.4\pm 0.7\) & \(8388\pm 1366\) \\ \hline \end{tabular}
\end{table} 
Table 3: MoEdyn average values in wet and dry conditions. Figures 7 and \(8\) show the relationship between MoEdyn and, respectively, wood density and wave velocity in the wet condition, whereas Figures 9 and 10 show the same relationship in the dry condition.