## 3 Results  
The first stage of preliminary studies aimed at evaluating the velocities of longitudinal and shear waves and estimating the angle of incidence (critical angle) to generate Lamb waves in boards. Assuming that the velocity of the antisymmetric Lamb wave \(c_{Lamb}^{plate}\) for the mode (A0) is close to the shear wave velocity in the board's materials, the critical angles of the Lamb waves (\(\alpha_{c}\)) for both materials were determined based on the Snell's Law, [39; 40]:  
\[\alpha_{c}=arcsin\Bigg{(}\frac{c^{air}}{c_{Lamb}^{plate}}\Bigg{)} \tag{1}\]  
where \(c^{air}\) is the speed of sound in air (about 340 m/s). The calculated values of the critical angles at 30 kHz were approximate \(\sim\)28\({}^{\circ}\) for polyamide and \(\sim\)30\({}^{\circ}\) for polyethylene board and are summarized in Table 2.  
Knowing the critical angles for both materials, the second part of the preliminary tests was focused on evaluating the attenuation coefficient and velocity as a function of the frequency of the Lamb wave in the boards. Figure 7 compares measured and theoretical velocity dispersion curves of Lamb waves (A0 mode) in the boards (PA6 and PE) in the frequency range from 25 kHz to 70 kHz. The theoretical curves were determined by well-known dispersion relationships for Lamb waves (A0 mode) published elsewhere [13; 39; 41]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Input Parameter** & **Unit** & **PA6** & **PE** \\ \hline The velocity of longitudinal wave & (m/s) & 2551 \(\pm\) 10 & 2338 \(\pm\) 10 \\ \hline The velocity of the shear wave & (m/s) & 1053 \(\pm\) 10 & 968 \(\pm\) 10 \\ \hline Critical angle & (\({}^{\circ}\)) & 28 & 30 \\ \hline Velocity of Lamb wave A0 mode @30 kHz & (m/s) & 760 \(\pm\) 10 & 695 \(\pm\) 10 \\ \hline Attenuation coefficient of Lamb wave A0 mode @30 kHz & (dB/m) & 13 \(\pm\) 1 & 28 \(\pm\) 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Measured wave properties of PA6 and PE within preliminary tests. Table 2 summarizes the results of the preliminary measurements for the respective frequency ranges. Compared to polyethylene, the polyamide board shows higher wave Lamb velocity and attenuation. Following the preliminary tests, the main ultrasonic experiments, using the noncontact ultrasonic technique, were conducted for the boards with simulated defects. First, the crack was placed at the edge of the board parallel to its surface (delamination). Figure 8a,b show the maximum amplitudes (absolute values) of the ultrasonic signals as a function of position measured for polyethylene and polyamide boards using a 30 kHz transducer. The results are shown for the \"healthy\" boards and the boards with defects of selected lengths of 3, 5, 10, and 15 mm. The amplitudes of Lamb waves for all measured defect lengths (in the range from 1 to 35 mm) and two frequencies, 30 kHz and 50 kHz, are presented in the Supplementary Materials (Figures S1 and S2). It is worth noting that the signal amplitudes measured in the polyethylene boards are nearly 130 mV higher than in polyamide. This can be attributed to the higher attenuation of ultrasonic waves in polyamide boards (see Table 2). Moreover, focusing on the wave amplitudes close to the board's edge (marked by the red widows in Figure 8a,b), it is visible that even small delamination (3 mm in depth) leads to a significant decrease in signal amplitude in both materials. In the case of polyethylene, a 5 mm delamination led to a decrease in the amplitude by approx. 2 dB, while for polyamide nearly 5 dB. Figure 8: Amplitude vs. probe position for delaminated boards. (**a**) Polyethylene. (**b**) Polyamide. The red box represents the area where defects were generated. Figure 7: Phase velocity of Lamb wave (of A0 mode) as a function of frequency. Predictions of the theory (“-” and “-”) vs. experimental results obtained for the tested boards: polyamide (\(\square\)) and polyethylene (\(\square\)). The second kind of (simulated) defect was a crack placed at the board's edge perpendicular to its surface.