Fig. 9

An example of an air flow (case 6a). \(V = 12\) \(\text{ cm}^3\) bubble bursts while it is rising in a suspension of \(\phi = 0.4\). a Time-lapse images (see Additional file 5: Movie 5). b Waveform (raw data) of the airwave recorded by 2 microphones. \(\times\) and \(\bigcirc\) correspond to the times indicated in (a). The pink \(\triangleright\) and \(\triangleleft\) indicate the times when the aperture radius \(R_{\mathrm{a}}\) was measured. c Spectrogram (time window 16.384 ms, overlap 16.3 ms) of Mic 1 (lower) data shown in (b). \(\triangleright\) and \(\triangleleft\) indicate \(f_{\mathrm{H}} =\) 870 and 2161 Hz, calculated from Eq. (11) using \(R_{\mathrm{a}}\) measured at the respective times shown in (b). The pink arrow indicates the Helmholtz resonance excited after bursting