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The Influence of Radiation Damping on ThroughResonance Variation in the Scattering CrossSection of Gas Bubbles
When a gas bubble in water undergoes forced pulsations, sound is radiated at the forcing frequency, and the scattering crosssection 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 throughresonance frequency dependence of the scattering and extinction crosssections, 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 crosssection to increase with increasing frequency through resonance. In 1977, Medwin published ‘Acoustical determination of bubblesize 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 AndreevaWeston 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.

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2 

Effects of Compressibility on the Radiation and Viscous Damping Terms in the Scattering and Extinction CrossSections of a Single Spherical Bubble: A Puzzle Solved and a Puzzle Posed
In [M. A. Ainslie & T. G. Leighton, Underwater Acoustic Measurements (Heraklion, Crete, 2007), pp 571576], the authors described a discrepancy between the radiation damping coefficients in the models due to Weston and to Medwin describing the scattering crosssection of a single spherical bubble. The resolution of that discrepancy [M. A. Ainslie & T. G. Leighton, J. Acoust. Soc. Am. 126, 21632175 (2009)] is summarised, and a new question posed related to viscous damping, as follows. The usual derivation of bubble damping due to viscosity assumes an incompressible medium; in that derivation, dilatational viscosity is neglected on the grounds that there is no compression. Modern theoretical treatments of scattering and attenuation through bubble clouds permit a compressible medium for radiation damping, but do not revisit the effect of this compressibility on the viscous damping. This raises as yet unanswered questions about the validity of the currently accepted expressions for the viscous damping factor used for calculating scattering and extinction crosssections

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[Abstract]
