A simplified expression is presented for predicting the absorption of sound in sea water, retaining the essential dependence on temperature, pressure, salinity, and acidity of the more complicated formula on which it is based [R. E. Francois and G. R. Garrison, “Sound absorption based on ocean measurements. Part II: Boric acid contribution and equation for total absorption,” J. Acoust. Soc. Am. 72, 1879–1890 (1982)]. The accuracy of the simplified formula is demonstrated by comparison with the original one for a range of oceanographic conditions and frequencies between 100 Hz and 1 MHz.

Eight experimentally controlled exposures to 1À2 kHz or 6À7 kHz sonar signals were conducted with four killer whale groups. The source level and proximity of the source were increased during each exposure in order to reveal response thresholds. Detailed inspection of movements during each exposure session revealed sustained changes in speed and travel direction judged to be avoidance responses during six of eight sessions. Following methods developed for Phase-I clinical trials in human medicine, response thresholds ranging from 94 to 164 dB re 1 lPa received sound pressure level (SPL) were fitted to Bayesian dose-response functions. Thresholds did not consistently differ by sonar frequency or whether a group had previously been exposed, with a mean SPL response threshold of 142 6 15 dB (mean 6 s.d.). High levels of between-and within-individual variability were identified, indicating that thresholds depended upon other undefined contextual variables. The dose-response functions indicate that some killer whales started to avoid sonar at received SPL below thresholds assumed by the U.S. Navy. The predicted extent of habitat over which avoidance reactions occur depends upon whether whales responded to proximity or received SPL of the sonar or both, but was large enough to raise concerns about biological consequences to the whales.

Perhaps the most familiar concepts when discussing acoustic scattering by bubbles are the resonance frequency for bubble pulsation, the bubbles' damping, and their scattering and extinction cross-sections, all of which are used routinely in oceanography, sonochemistry, and biomedicine. The apparent simplicity of these concepts is illusory: there exist multiple, sometimes contradictory definitions for their components. This paper reviews expressions and definitions in the literature for acoustical cross-sections, resonance frequencies, and damping factors of a spherically pulsating gas bubble in an infinite liquid medium, deriving two expressions for "resonance frequency" that are compared and reconciled with two others from the reviewed literature. In order to prevent errors, care is needed by researchers when combining results from different publications that might have used internally correct but mutually inconsistent definitions. Expressions are presented for acoustical cross-sections associated with forced pulsations damped by liquid shear and (oft-neglected) bulk or dilatational viscosities, gas thermal diffusivity, and acoustic re-radiation. The concept of a dimensionless "damping coefficient" is unsuitable for radiation damping because different cross-sections would require different functional forms for this parameter. Instead, terms based on the ratio of bubble radius to acoustic wavelength are included explicitly in the cross-sections where needed.

Long-range acoustic propagation in isothermal conditions is considered, involving multiple reflections from the sea surface. If the sea is calm there is almost perfect reflection and hence little loss of acoustic energy or coherence. The effect of wind is to increase propagation loss due to rough surface scattering and the interaction with near-surface bubble clouds. Previously published measurements of wind-related attenuation in shallow water, at a fixed range of 23km, are converted to surface reflection loss by dividing the total attenuation by the expected number of surface interactions. Theoretical predictions of coherent reflection loss are compared with these measurements in the frequency range 0.9–4.0kHz and wind speeds up to 13m∕s. Apart from an unexplained seasonal dependence, it is shown that the magnitude of the predicted rough surface scattering loss is sufficient to explain the measurements if the effect of bubbles is included, and not otherwise. The bubbles are found to play an important catalytic role, not by scattering or absorbing sound, but by refracting it up towards the sea surface and thus enhancing the scattering loss associated with the rough air–sea boundary. Possible explanations for the apparent seasonal variations in the measurements are explored.

The scattering cross-section sigma(s) of a gas bubble of equilibrium radius R(0) in liquid can be written in the form sigma(s)=4piR(0) (2)[(omega(1) (2)omega(2)-1)(2)+delta(2)], where omega is the excitation frequency, omega(1) is the resonance frequency, and delta is a frequency-dependent dimensionless damping coefficient. A persistent discrepancy in the frequency dependence of the contribution to delta from radiation damping, denoted delta(rad), 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 delta(rad) on frequency, a result which Medwin [Ultrasonics 15, 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 delta(rad) 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.