## 5 Results and Discussion  
### Polystyrene (PS)  
PS was tested for its moderate values of bulk-wave attenuation coefficients, \(\alpha_{\rm L}\) = 39.0 dB/m/MHz and \(\alpha_{\rm T}\) = 113 dB/m/MHz. These were obtained using the methods described previously [44; 45]. Two 1.38-mm thick sheets were used to obtain Lamb-wave attenuation. These two sheets were from different sources several years apart. Parts of the tests were described in Section 3 as an example. Their properties are listed in Table 1 as G1a and G1b. Figure 5a,b show \(\alpha\)-S and \(\alpha\)-A for PS sheets of 1.38-mm thickness in blue (for symmetric mode) and red (for asymmetric mode) symbols, respectively. In Figure 5a, two sets of \(\alpha\)-S values are plotted in dots and + symbols from 140 to 600 kHz, and calculated values of \(\alpha\)-S\({}_{\rm 0}\) are plotted in a solid blue curve. Blue and red dashed lines representing the bulk-wave attenuation coefficients \(\alpha_{\rm L}\) and \(\alpha_{\rm T}\) are also shown. The Lamb-wave velocity range of these datasets ranged from 2.1 to 0.7 mm/us. The A\({}_{\rm 0}\) mode contribution was excluded by cutting off the low-speed portion of the WT intensity. The slow-moving S\({}_{\rm 0}\) mode at 650 kHz had no WT intensity and was not included in the WT analysis. Other modes did not exhibit WT intensity that can be analyzed for attenuation. Both of the observed \(\alpha\)-S data matched well with the calculated \(\alpha\)-S\({}_{\rm 0}\) curve to their respective high-frequency limit of 526 and 600 kHz. That is, the observed values are of the \(\alpha\)-S\({}_{\rm 0}\) mode. Figure 5: (a) \(\alpha\)-S\({}_{\rm 0}\) for PS sheets of 1.4-mm thickness in blue symbols. \(\alpha\)-S values plotted in dots used Olympus V101 as Tx and + symbols NDT C16 as Tx. KRN-BB-PC was Rx for both. Calculated values of \(\alpha\)-S\({}_{\rm 0}\) are plotted in a solid blue curve. Blue and red dashed lines are the bulk-wave attenuation coefficients, \(\alpha_{\rm L}\) and \(\alpha_{\rm T}\). Vertical bar indicates twice the value of average deviation or 2 \(\times\) dev. (b) \(\alpha\)-A\({}_{\rm 0}\) for PS sheets of 1.4-mm thickness in red symbols. Tx for all three sets used NDT C16 at 60\({}^{\circ}\) incident angle. KRN-BB-PC was Rx for all three. Calculated values of \(\alpha\)-A\({}_{\rm 0}\) are plotted in a solid red curve. Blue and red dashed lines are the bulk-wave attenuation coefficients, \(\alpha_{\rm L}\) and \(\alpha_{\rm T}\). Vertical bar shows 2 \(\times\) dev. Figure 5b gives \(\alpha\)-A values from two tests. Calculated values of \(\alpha\)-A\({}_{0}\) in a solid red curve and the \(\alpha_{\rm L}\) and \(\alpha_{\rm T}\) dashed lines in blue and red are also plotted. The velocity range of these datasets was from 1.2 to 0.6 mm/us, excluding the faster S\({}_{0}\) mode. Differences of the two-sided signals were used to minimize the symmetric components. Both \(\alpha\)-A attenuation data showed gradual increase straddling the calculated \(\alpha\)-A\({}_{0}\) (red curve), which nearly overlaps the red-dash \(\alpha_{\rm T}\) line. The observed attenuation values ranged from 140 to 700 kHz. These deviated from the predicted values by as much as 15 dB/m (or 27% at 500 kHz), but the overall trend followed the calculated attenuation curve. The agreement between theory and experiment is deemed moderately good. In order to estimate the accuracy of the attenuation values obtained, deviation from the predicted value at the same frequency was calculated for each measurement. This is defined as the magnitude of the difference between the predicted and observed values. Percent deviation was also obtained. For this procedure, the predicted \(\alpha\)-S\({}_{0}\) values were fitted to a fourth order polynomial in frequency, whereas \(\alpha\)-A\({}_{0}\) values were represented by \(\alpha_{\rm T}\) values, as these two are close to each other. Results of the averaged deviation and percent deviation are as follows: