The sound fields resulting from a plane wave incident on a spherical elastic shell are found. Both the internal and external fields due to the shell are considered and compared with well-known results. The Rayleigh limit is discussed, and it is found that the external field is similar to that produced by a rigid sphere but with more complicated coefficients. The internal field is of a complicated nature but reasonable to consider for numerical computation. The sound fields for a hemispherical shell mounted on a rigid medium are obtained by the image method. Numerical results for the sound intensity at the center of the hemisphere are presented for various elastic materials.

A precise theory exists, based on an integral equation, by which acoustic signal attenuation versus frequency, due to a known bubble-density distribution versus bubble radius, may be calculated. Lacking a simple inversion scheme for the integral equation, an approximation which accounts only for attenuation due to resonant bubbles is available (and often applied) to calculate a bubble distribution. An iterative approach for improving on that resonant bubble approximation is presented here. That new approach is based on alternating calculations and corrections between attenuation data and the bubble distribution presumed to have produced it. This iterative technique is tested, first, on two simulated data sets of bubble distributions. It is then applied to attenuation data measured as a function of frequency from 39 to 244 kHz during the Scripps Pier Experiment [Caruthers et al., Proc. 16th Int. Cong. on Acoust., pp. 697–698 (1998)]. The results of the simulations demonstrate the validity of the method by faithfully reproducing the initial distributions for the simulated attenuation data. When applied to the real data, the method leads to a bubble distribution whose use in a direct solution of the integral equation reproduces the measured data with greater accuracy than does the resonant bubble approximation alone.

No abstract

An experiment was performed just off the research pier at the Scripps Institute of Oceanography to determine the acoustic effects of small bubbles in very shallow water (∼6 m depth). The distance offshore was ∼300 m. The propagation lengths were 2–10 m, and the frequency range was from 39 to 244 kHz. During the experiment, rip currents passed through the field of measurement instruments. These rip currents were laden with bubbles created in the surf between the instruments and the shore. The effects of these rip currents on the spatial distributions of the resulting acoustic attenuation are discussed. From the attenuation data, the bubble distributions are calculated using a new iterative approach [Caruthers et al., in press, J. Acoust. Soc. Am.] that is based on the well-known resonant bubble approximation. Calculated bubble distributions varied from an essentially uniform lack of bubbles during quiescent periods to highly inhomogeneous and dense bubbly regions within rip events. Such observed distributions were consistent with measurements made by other investigators during the experiment.