The Influence of Radiation Damping on Through-Resonance Variation in the Scattering Cross-Section of Gas Bubbles

When a gas bubble in water undergoes forced pulsations, sound is radiated at the forcing frequency, and the scattering cross-section exhibits a resonance peak when the forcing frequency passes through the bubble’s natural frequency. At resonance, the amplitude of the scattered spherical wave is determined by the amount of damping associated with the bubble dynamics. In his 1967 article, ‘Sound propagation in the presence of bladder fish’, Weston describes a model for the through-resonance frequency dependence of the scattering and extinction cross-sections, based on the work of Andreeva (1964). In Weston’s model, if all damping terms other than radiation damping are omitted, the resonance peak is skewed, with a tendency for the scattering cross-section to increase with increasing frequency through resonance. In 1977, Medwin published ‘Acoustical determination of bubble-size spectra’, based on Eller (1970), in which he describes a similar model, according to which the predicted resonance peak is also skewed, but in the opposite direction to that predicted by Weston. If Medwin’s model turns out to be valid, this would have little impact, as his curves are already in widespread use. However, if the Andreeva-Weston model is correct, a small adjustment becomes necessary to Medwin’s curves. A possible experiment designed to establish the true frequency dependence is described, involving the ensonification of a single spherical bubble with a broadband pulse, through the bubble’s resonance frequency. If the radiation damping can be separated form other effects, the correct frequency dependence can be established by measuring the spectrum of the scattered sound