## 5 Results and Discussion
### Soda Line Glass  
Two samples of soda line glass, 2-mm (G6a) and 4.7-mm (G6b) thick, were tested for Lamb-wave attenuation. The thicker plate appears to be of tempered grade from the edge finishing, but an optical polarization test was inapplicable because of its darkened color. Direct bulk-wave attenuation tests could not be conducted due to the size and thickness. Thus, the data of a thicker soda line glass of 5.6-mm thickness were used, namely, \(\alpha_{\rm L}=8.7\) dB/m/MHz and \(\alpha_{\rm T}=16.2\) dB/m/MHz (cf. Table 1). These are more than six times those of 410 SS in Section 5.3. For the 2-mm glass sheet, observed \(\alpha\)-S and \(\alpha\)-A values are given in Figure 12a,b, respectively. Calculated values are given for S\({}_{\rm o}\) and A\({}_{\rm o}\) modes in each figure, as well as the bulk-wave attenuation lines, as in the previous figures. In Figure 12a, observed values were mostly below the predicated curve up to 900 kHz, although the general trend followed the calculation. This behavior was also found in Figure 12b for the \(\alpha\)-A data. Deviations were larger in the asymmetric case than in the symmetric case. Calculation of \(\alpha\)-S and \(\alpha\)-A values relied on the bulk-wave attenuation of 5.6-mm thick glass plate, which was nearly three times the thickness of the sample used. Thus, the calculated values may be overestimated. When one assumes \(\alpha_{\rm L}=4\) dB/m/MHz and \(\alpha_{\rm T}=8\) dB/m/MHz, the calculated values are approximately halved (indicated by dotted curves in Figure 12a,b). The blue dotted curve in Figure 12a matched the observed data well. The red dotted curve for \(\alpha\)-A in Figure 12b was slightly above the lower limits of the observed values, indicating that the \(\alpha_{\rm T}\) value needed to be slightly higher. Further refinements are possible by adjusting the assumed values of \(\alpha_{\rm L}\) and \(\alpha_{\rm T}\). Presently, low levels of bulk-wave attenuation, as assumed above, cannot be measured for 2-mm thick glass. However, \(\alpha\)-S and \(\alpha\)-A can be obtained as shown here. In turn, these can be used to estimate bulk-wave attenuation of thin sheet materials. This approach is based on the Disperse calculation, verified using moderate to high attenuating plate samples. Figure 13a,b show observed \(\alpha\)-S and \(\alpha\)-A values for 4.7-mm glass plate along with the calculated attenuation. For the symmetric case, \(\alpha\)-S values follow the calculated \(\alpha\)-S\({}_{\rm o}\) curve up to 550 kHz, with the observed values always being lower than the calculated curve. Above 650 kHz, the observed values were close to the calculated \(\alpha\)-S\({}_{\rm 1}\) curve, again being lower than the prediction. In Figure 12b for the asymmetric case, the observed data followed the calculated \(\alpha\)-A\({}_{\rm o}\) curve up to 1000 kHz. The data did not match the plotted A\({}_{\rm 1}\)-mode attenuation between 400 and 800 kHz. For this glass plate, the values of \(\alpha_{\rm L}\) and \(\alpha_{\rm T}\) used in theoretical calculation were appropriate, although the \(\alpha\)-S\({}_{\rm o}\) values were always below the prediction. However, increasing \(\alpha_{\rm T}\) will cause the calculated \(\alpha\)-A\({}_{\rm o}\) curve to move above the observed data points. This inconsistency appeared in other cases as well, e.g., Al-7475 sheet (and PVC plate to be discussed subsequently). Although it is immaterial to consider deviation statistics for these tests for low attenuation glasses, deviation and percent deviation were calculated. For the 2-mm glass sheet, the predicted \(\alpha\)-S\({}_{\rm o}\) values were fitted to a third order polynomial in frequency, and \(\alpha\)-A\({}_{\rm o}\) values were fitted to a linear equation. Averaged results are as follows: \begin{tabular}{c c c c} \hline \hline Wave Mode & Deviation (dB/m) & Percent Deviation (\%) & Data Count \\ \hline Symmetric case 2 mm: & 2.98 & 44.9 & 46 \\ \hline Asymmetric case 2 mm: & 3.24 & 34.0 & 57 \\ \hline \hline \end{tabular}