Bubble acoustical scattering cross section under multi-frequency acoustic excitation**Project supported by the National Natural Science Foundation of China (Grant No. 11674074) and the Program for Changjiang Scholars and Innovative Research Team in University, China (Grant No. IRT1228).

Abstract

The acoustical scattering cross section is usually employed to evaluate the scattering ability of the bubbles when they are excited by the incident acoustic waves. This parameter is strongly related to many important applications of performance prediction for search sonar or underwater telemetry, acoustical oceanography, acoustic cavitation, volcanology, and medical and industrial ultrasound. In the present paper, both the analytical and numerical analysis results of the acoustical scattering cross section of a single bubble under multi-frequency excitation are obtained. The nonlinear characteristics (e.g., harmonics, subharmonics, and ultraharmonics) of the scattering cross section curve under multi-frequency excitation are investigated compared with single-frequency excitation. The influence of several paramount parameters (e.g., bubble equilibrium radius, acoustic pressure amplitude, and acoustic frequencies) in the multi-frequency system on the predictions of scattering cross section is discussed. It is shown that the combination resonances become significant in the multi-frequency system when the acoustic power is big enough, and the acoustical scattering cross section is promoted significantly within a much broader range of bubble sizes and acoustic frequencies due to the generation of more resonances.