Fig. 16

Peak frequency \(f_{\mathrm{p}}\), decay rate \(\beta\) (both with errors) vs. air column length L. a \(f_{\mathrm{p}}\) vs. L of airwaves excited by a \(V = 5\) \(\text{ cm}^3\) bubble bursting in a suspension of \(\phi = 0.4\). A green curve indicates \(f_{\mathrm{A}}\) (Eq. (20)). Pink lines indicate \(f_{\mathrm{H}}\) (Eq. (11)) calculated using \(R_{\mathrm{a}}\) values given in the legend. b \(\beta\) vs. L; otherwise the same as (a). A green curve indicates the decay rate \(\beta _{\mathrm{a}}\) (Eq. (21)). Pink lines indicate \(\beta _{\mathrm{r}} + \beta _{\mathrm{vt}}\) (Eqs.(13), (14)) calculated using \(R_{\mathrm{a}}\) values given in the legend. \(R_{\mathrm{a}}\) is chosen to calculate the minimum and maximum values of \(\beta _{\mathrm{r}} + \beta _{\mathrm{vt}}\) in the range of \(R_{\mathrm{a}} = 1.1 - 2.5\) mm used in (a)