Index of content:
Volume 126, Issue 5, November 2009
- GENERAL LINEAR ACOUSTICS 
Near resonant bubble acoustic cross-section corrections, including examples from oceanography, volcanology, and biomedical ultrasound126(2009); http://dx.doi.org/10.1121/1.3180130View Description Hide Description
The scattering cross-section of a gas bubble of equilibrium radius in liquid can be written in the form , where is the excitation frequency, is the resonance frequency, and is a frequency-dependent dimensionless damping coefficient. A persistent discrepancy in the frequency dependence of the contribution to from radiation damping, denoted , is identified and resolved, as follows. Wildt’s [Physics of Sound in the Sea (Washington, DC, 1946), Chap. 28] pioneering derivation predicts a linear dependence of on frequency, a result which Medwin [Ultrasonics15, 7–13 (1977)] reproduces using a different method. Weston [Underwater Acoustics, NATO Advanced Study Institute Series Vol. II, 55–88 (1967)], using ostensibly the same method as Wildt, predicts the opposite relationship, i.e., that is inversely proportional to frequency. Weston’s version of the derivation of the scattering cross-section is shown here to be the correct one, thus resolving the discrepancy. Further, a correction to Weston’s model is derived that amounts to a shift in the resonance frequency. A new, corrected, expression for the extinction cross-section is also derived. The magnitudes of the corrections are illustrated using examples from oceanography, volcanology, planetary acoustics, neutron spallation, and biomedical ultrasound. The corrections become significant when the bulk modulus of the gas is not negligible relative to that of the surrounding liquid.