Sound attenuation in high mach number oscillating bubble media

We study theoretically and numerically sound attenuation in bubble-containing media when the bubbles are freely oscillating at high Mach numbers. This paper expands one of the main forms of bubble-related acoustic damping factors by extending the previous theories to higher Mach numbers, further improves the theories of nonlinear sound propagation in bubble-containing media. A nonlinear sound propagation model incorporating second-order liquid compression terms is developed, expressing the sound velocity and density in the medium as a function of the driving pressure, and taking into account the higher-order liquid compression effects on sound propagation. The correctness of the proposed model is verified by comparing with a linear model and a nonlinear model containing only low-order Mach number terms. When the bubble oscillates at a high Mach number, radiation damping, which is directly related to Mach number, becomes the main damping component affecting sound attenuation. The higher the driving amplitude, the stronger the nonlinear effect, and the greater the impact of high-order liquid compression effects on the sound attenuation, the more necessary it is to use the proposed model to calculate the sound attenuation. For high Mach numbers, varying the bubble radius and bubble number density, respectively, the difference between the proposed model and the model containing only low-order Mach number terms in capturing the pressure-dependent attenuation is calculated. Due to stronger radiation damping in smaller bubbles, the effect of compressibility becomes more important. The smaller the bubble radius, the greater the half-quality factor of the curve related to the difference in attenuation calculated by the two models, the more necessary it is to calculate the pressure-dependent attenuation using the proposed model. Here, the half-quality factor is defined as the corresponding frequency bandwidth when the curve falls from the maximum value to 22 times. Without considering the coupling effect between bubbles, the half-quality factor of the curve is not affected by the bubble number density.