Naval Res. Lab., Stennis Space Center, MS 39529-5004
The classic theory of sound propagation in bubbly water incorrectly describes the properties of dense media containing resonating bubbles of uniform size. It assumes that the bubbles oscillate independently. However, resonating bubbles are strongly coupled by acoustic radiation, and acoustic propagation can be fully explained only in terms of the collective action of the medium, which is dominated by the ``symmetric'' normal mode. In this work, the propagational characteristics of bubbly water are determined by averaging the ensemble behavior of the symmetric mode over distributions of bubble sizes and locations. All orders of multiple scattering are included, and ``shadowing'' effects incorporated. New theoretical expressions for the phase speed and attenuation are presented. Comparisons between theory and experimental data are made by integrating multiple scattering effects over a ``region of collective interaction'' around the bubbles. For uniformly size bubbles, a downward frequency shift and suppression of the attenuation peak is observed, which is more pronounced for higher volume fractions. The phase speed is also modified. In water containing may differently sized bubbles, multiple scattering typically plays a much smaller role in determining acoustic properties, and the classic theory of propagation is adequate.