## 5 Results and Discussion
### Summary of Lamb-Wave Attenuation  
Lamb-wave attenuation data obtained in this study are summarized in Table 2. Data for Al-7475 and 410 SS were omitted as their reliability is low. Theoretically predicted (Theory) and experimentally observed (Exp.) \(\alpha\)-S\({}_{\text{o}}\) and \(\alpha\)-A\({}_{\text{o}}\) values at near the middle of the frequency range of measurement for 11 sheets and plates are listed with bulk-wave attenuation coefficients and thickness. The observed attenuation values were averaged over \(\pm\)5 kHz of the indicated frequency. In all cases, a comparison of theory and experiment at the mid-frequency produced a closer pairing than the previously listed deviation statistics. This is mainly due to large attenuation value differences at low and high ends of the frequency range. Still, the maximum percent deviation reached 20% (PMMA and HDPE), showing the need of additional study. Two experimental approaches can improve Lamb-wave attenuation data to remove the uncertainty of contact sensing. One is to raise the pulse driving voltage in combination with an arbitrary waveform generator. Power amplifiers to 1 MHz are available commercially, producing \(\pm\)300 V output into an ultrasonic transducer. For generating sub-MHz Lamb waves, ultrasonic transducers are better suited than a high-power laser. The other approach is to increase the length and width of samples of multiple thicknesses in low attenuation materials. It is important to have similar dimensions in the length and width because side reflections present serious interference in rectangular shapes. As for thicknesses, a thin sheet under 3-mm thickness expands the frequency range of the zeroth order modes, whereas a plate of a few times the thickness of the thin sample covers higher order modes at frequencies below 1 MHz. However, it is currently impossible to determine the bulk-wave attenuation coefficients on a thin plate with desired accuracy when the \(\alpha_{\text{L}}\) and \(\alpha_{\text{T}}\) values are under approximately 10 dB/m/MHz. Next, the peak amplitude of received signals is summarized. Results are given in Table 3. Sample designation was the same as before, and the transmitter used and peak displacement in nanometers are listed for both wave modes, symmetric and asymmetric. Because of the use of calibrated point contact sensors (KRN-BB-PC), a quantitative comparison is possible in peak displacement, which ranged from 10 pm to 1.5 nm. The signals used in this comparison were chosen at the propagation distance of 200 mm, using the same receiving sensor. The calibration was against Rayleigh-wave motion, which is similar to Lamb-wave motion and generated vertical displacement that excited the KRN sensor [50]. The receiving sensitivity to Rayleigh waves was approximately 10 dB lower than that for normally incident waves. Lower peak-displacement values were found for tests with highly attenuating media, such as PMMA, PVC, and HDPE. Generally, Al, steel, and glass had higher values, but the peak levels varied. A part of this variation must be from the coupling of the transmitter to a plate. For attenuation measurements, maximizing Lamb-wave intensity is not critical as long as stable and adequate coupling is established.