## 3 Results and Discussion
The temporal evolution of the upstream secondary bubble clouds and the change in \(R_{\text{max2}}\) relative to \(T_{\text{osc1}}\) are plotted in Figure 5. For different-sized laser bubbles, both the first and second generations of secondary bubble clouds formed within approximate fixed time ranges, indicating a stable time range for the vibrational rarefaction wave generation. It is essential to mention that the time range for the second generation of secondary bubble clouds might become disrupted for exceptionally large laser bubbles, due to the shift in the coupling between the laser bubble oscillations and liquid-mass oscillations, which was discussed in our previous work [25] but falls outside the scope of the current study. This study showed that the time for the first peak of \(A_{\text{tot}}\) to be reached increased from 103 \(\upmu\)s for \(h=27\) mm to 108 \(\upmu\)s for \(h=32\) mm, and further to 126 \(\upmu\)s for \(h=37\) mm. Correspondingly, the intervals between adjacent peaks increased from 124 \(\upmu\)s for \(h=27\) mm to 139 \(\upmu\)s for \(h=32\) mm, and finally to 167 \(\upmu\)s for \(h=37\) mm, as displayed in Figure 5a. Despite the maxima peaks of \(R_{\text{max2}}\) being shifted towards the right with increasing liquid height, the modulation period of \(R_{\text{max2}}\) (\(T_{\text{osc1}}\)) remained constant at a value of 80 \(\upmu\)s for \(h=27\) mm and 32 mm, with a slight increase to 86 \(\upmu\)s for \(h=37\) mm, as shown in Figure 5b. In general, with the increase in the liquid height within the same cuvette, the laser bubble showed an approximate constant modulation period of \(R_{\text{max2}}\) (\(T_{\text{osc1}}\)) and the secondary bubble clouds depicted a remarkable increase in the time interval between adjacent generations. This indicates the change in liquid has a strong influence on the interval of adjacent rarefaction waves while barely influencing the period of each rarefaction wave. Next, the influence of the cuvette's inner size on the rarefaction waves and cavitation dynamics was studied. In this case, the liquid height was maintained at a constant value of 27 mm, while the inner size of the cuvette varied from 10 mm to 12 mm. This adjustment simultaneously introduced changes to both the properties of the elastic wall and the liquid mass. The comparison of the secondary bubble dynamics and the variations in \(R_{\text{max2}}\) (\(T_{\text{osc1}}\)) between these configurations is shown in Figure 6.  
With the progressive increase in the cuvette's inner size, we observed a significant augmentation in both the peak-to-peak intervals for secondary bubble clouds and the modulation period of \(R_{\text{max2}}\) (\(T_{\text{osc1}}\)) for the laser bubble. Specifically, for cuvettes with inner sizes increasing from 10 mm to 11 mm and 12 mm, the peak-to-peak interval increased from 124 \(\upmu\)s to 144 \(\upmu\)s and 162 \(\upmu\)s, while the modulation period of \(R_{\text{max2}}\) (\(T_{\text{osc1}}\)) increased from 80 \(\upmu\)s to 100 \(\upmu\)s and 116 \(\upmu\)s, respectively. The changes in the modulation period with cuvette inner size indicate that the wall determines the period of each vibrational rarefaction wave. As for the increase in the peak-to-peak interval, it can be attributed to the increase of the liquid volume. The onset time of vibrational wave \(t_{0}\) changes in both cases. For the case with varying liquid height in the same cuvette, it increased from 63 \(\upmu\)s for \(h=27\) mm, to 68 \(\upmu\)s for \(h=32\) mm, and finally to 83 \(\upmu\)s for h = 37 mm, respectively. For the case with varying cuvette size under the same liquid height, it increased from 63 \(\upmu\)s for \(d=10\) mm to 66 \(\upmu\)s for \(d=11\) mm and 78 \(\upmu\)s for \(d=12\) mm. This indicates a strong relevance between the onset time of the tensile rarefaction wave and the liquid parameters. Table 1 provides a summary of the key vibrational rarefaction wave parameters associated with the cuvette size and the liquid volume.