## 3 Results and Discussion
Our findings demonstrate that \(T_{\text{wall}}\) is predominantly influenced by the cuvette wall, whereas \(t_{0}\) and \(T_{\text{lm}}\) are mainly influenced by the liquid. These observations underscore that the vibrational pressure series directly originates from the periodic vibrations of the wall, which are consistently triggered by the pressure elevation resulting from the expansion of the laser bubble and the subsequent oscillations in the surrounding liquid. For a damped vibrating structure, its eigenfrequency is determined by inherent characteristics such as quality, stiffness, geometry structure, and damping coefficient. When \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Cuvette Inner Size \(d\) (mm)**} & \multirow{2}{*}{**Liquid Height \(h\) (mm)**} & \multirow{2}{*}{**Liquid Volume \(V\) (mm\({}^{3}\))**} & \multicolumn{4}{c}{**Vibrational Rarefaction Wave Parameters**} \\ \cline{4-5}  & & & **\(t_{0}\) (μs)** & \(T_{\text{wall}}\) (μs) & \(T_{\text{lm}}\) (μs) \\ \hline
10 & 27 & 2700 & 63 & 80 & 124 \\
10 & 32 & 3200 & 68 & 80 & 139 \\
10 & 37 & 3700 & 83 & 86 & 167 \\
11 & 27 & 3267 & 66 & 100 & 144 \\
12 & 27 & 3888 & 78 & 116 & 162 [25] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristic parameters of vibrational rarefaction waves corresponding to the wall and liquid. Figure 6: The temporal evolution of secondary bubble clouds (**a**) and the evolution of \(R_{\text{max2}}\) concerning \(T_{\text{osc1}}\) (**b**) for cuvettes with different inner sizes. \(h=27\) mm. I for \(d=10\) mm, II for \(d=11\) mm, and III for \(d=12\) mm. Here, the \(T_{\text{lm}}\) and \(T_{\text{wall}}\) in the case of \(h=27\) mm/\(d=12\) mm were mentioned in [25]. simplifying it to a one-dimensional mass-spring-damper model, the eigenperiod is positively related to the mass and damping coefficient [45]. Consequently, in this work, an increase in the liquid volume (mass) directly leads to a lengthening of the period of liquid-mass oscillation. This, in turn, resulted in an increased time interval between the adjacent waves. However, it is noteworthy that the eigenperiod of vibrational pressure remains approximately constant because the same cuvette is used, and the slight increase observed in \(T_{\text{wall}}\) for \(h=37\) mm case may be linked to a minor rise in the damping coefficient of wall vibrations induced by the increased liquid height. This can explain the approximate constant modulation period of \(R_{\text{max}}\) (\(T_{\text{osc1}}\)) and the increase in the peak-to-peak interval between adjacent secondary bubble clouds. On the other hand, the increase in cuvette inner size with the same liquid height is accompanied by both the increase in the mass of the cuvette wall and the liquid. Consequently, this leads to the increase in the eigenperiods of both the wall vibrations and liquid-mass oscillations and thus to both the increase in the period of each rarefaction wave and in the time interval between adjacent waves. It is important to highlight that when comparing two scenarios--one with \(d=10\) mm/h = 37 mm and the other with \(d=12\) mm/\(h=27\) mm--the latter case, even though it possesses a larger liquid volume of 3888 mm\({}^{3}\), shows a shorter period of liquid-mass oscillation when compared to the former case with 3700 mm\({}^{3}\). This discrepancy can be attributed to the significant alteration in the liquid geometry, underscoring the crucial role it plays in determining the eigenperiod of the liquid-mass oscillation system, which has multiple degrees of freedom [45]. Another intriguing aspect is the variation in the onset time of the first vibrational pressure concerning liquid parameters. Remarkably, in all the cases, its value closely approximates to half of \(T_{\text{lm}}\).