## 5 Results and Discussion
### High-Density Polyethylene (HDPE)  
An HDPE plate of 7.1-mm thickness was tested for its \(\alpha\)-S and \(\alpha\)-A, as it also has high values of bulk-wave attenuation [44; 45]. The \(\alpha_{\rm L}\) and \(\alpha_{\rm T}\) values, listed in Table 1, were used for calculating Lamb-wave attenuation for comparison. Figure 17a,c show observed \(\alpha\)-S and \(\alpha\)-A values for the HDPE plate in blue and red symbols, respectively, together with the theoretical results. Identical test set-ups were used, but some discrepancies were found between the two sets. Because of high attenuation, special procedures had to be used in Disperse calculations for \(\alpha\)-S and \(\alpha\)-A, which were kindly conducted by [PERSON] In Figure 17a, two sets of \(\alpha\)-S\({}_{\rm o}\) values are given. The velocity range of these datasets was from 2.1 to 1.0 mm/\(\upmu\)s. These mostly followed the calculated curve for \(\alpha\)-S\({}_{\rm o}\), but one set showed larger deviations over 50-90 kHz. As previously observed for PVC, this region followed a straight line from 40 to 100 kHz. The origin of this behavior is unknown, but here another dataset did not show the same behavior, suggesting the straight-line increase is likely to be an erratic behavior from sensor coupling. Figure 17b shows \(\alpha\)-S values vs. frequency to 500 kHz. At frequencies above 120 kHz, only attenuation of higher modes was detected. For one test (shown in dots), test data followed the predicted \(\alpha\)-S\({}_{\rm 1}\) and \(\alpha\)-S\({}_{\rm 2}\) curves (shown in dotted and dashed curves) to 370 kHz. The other test showed slightly lower attenuation above 300 kHz, but joined the other curve above 370 kHz. The observed data followed theoretical prediction for \(\alpha\)-S\({}_{\rm 1}\) and \(\alpha\)-S\({}_{\rm 2}\) well. In the higher frequency ranges for S\({}_{\rm 1}\) to S\({}_{\rm 3}\) modes, however, spectrograms from WT analyses are always diffuse. Thus, the observed good agreement between theory and experiment is surprising and requires more extensive studies before a definitive conclusion can be drawn. Figure 16: (**a**) Observed \(\alpha\)-S\({}_{\rm o}\) values for 4.3-mm PVC plate along with the calculated attenuation and dashed lines for \(\alpha_{\rm L}\) and \(\alpha_{\rm T}\). Two test series are plotted using blue symbols. Both used Olympus V101 Tx and KRN-BB-PC Rx, with short-pulse excitation. Vertical bar shows 2 \(\times\) dev. (**b**) Observed \(\alpha\)-A\({}_{\rm o}\) values for 4.3-mm PVC plate along with the calculated attenuation and dashed lines for \(\alpha_{\rm L}\) and \(\alpha_{\rm T}\). Both series are plotted using red symbols and used NDT C16 Tx at 60\({}^{\circ}\) incident angle and KRN-BB-PC Rx. All with short-pulse excitation. Vertical bar shows 2 \(\times\) dev. Figure 17: (**a**) Observed \(\alpha\)-S\({}_{0}\) values for 7.1-mm HDPE plate with the calculated attenuation and dashed lines for \(\alpha_{\rm L}\) and \(\alpha_{\rm T}\). Two test series are plotted using blue symbols. Both used Olympus V101 Tx and KRN-BB-PC Rx, with short-pulse excitation. Vertical bar shows 2 \(\times\) dev. (**b**) Observed \(\alpha\)–S values for 7.1-mm HDPE plate along with the calculated attenuation and dashed lines for \(\alpha_{\rm L}\) and \(\alpha_{\rm T}\). Frequency range was extended to 500 kHz. Two test series and their symbols are identical to those in (**a**). Calculated attenuation curves included \(\alpha\)–S\({}_{1}\) (blue dotted curve) and \(\alpha\)–S\({}_{2}\) (blue short-dash curve). (**c**) Observed \(\alpha\)–A\({}_{0}\) values for 7.1-mm HDPE plate using red symbols. Dot data used NDT C16 Tx at 60\({}^{\circ}\) incident angle with 50-kHz single-cycle sinewave excitation and KRN-BB-PC Rx. The other two series used NDT C16 Tx at 60\({}^{\circ}\) incident angle with short-pulse excitation and KRN-BB-PC Rx. The calculated attenuation and dashed lines for \(\alpha_{\rm L}\) and \(\alpha_{\rm T}\) are also plotted. Vertical bar shows 2 \(\times\) dev.