Theory and experiment of the resonance sound wave interactions in water

Abstract

Equations governing nonlinear interactions among acoustic waves in water which satisfy the resonance conditions are derived from the Burgers equation. Taking into account of the second-order nonlinear, the three-wave interaction is the fundamental process of the interaction equations. Then, taking the three-wave interaction equation as an example, the energy transfer mechanism among the three acoustic waves is quantitatively analyzed. And the three-wave sound energy propagation is studied through numerical calculation. An interesting phenomenon is found that, when the three acoustic waves meet the relationship of a weak low-frequency sound and two strong high-frequency sounds, the energy of low-frequency sound will be amplified or reduced in some regions during the three-wave propagation. And the location and size of the regions are affected by the acoustic wave amplitude, frequency, and phase. The variation severities of low-frequency acoustic wave energy are mainly determined by other two high-frequency acoustic wave energy. The frequencies of two high-frequency sound waves have little effects on the energy of low-frequency sound wave. The region whether is amplification or reduction is determined by the phase difference of three waves. The variation laws of low-frequency sound energy are also verified by the experimental results in river.

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“…In this case, the secondorder nonlinear equation as a unit process will be three-wave interaction. Equations with second-order nonlinear terms can be analyzed by equations (Yang et al, 2014).…”

“…Its energy is spread over a large area. Sound waves propagating through water media will experience energy loss (Gheibi & Hedayat, 2020) caused by wave propagation, energy absorption, and reflections occurring at the waters' bottom or surface (Yang et al, 2014). In reality, the intensity level measured in this study is a sound wave that has experienced attenuation due to attenuation.…”

“…Resonating sound waves can be converted into energy and regressed in three modes. The description of the mathematical model in the interaction of sound waves can be derived as follows in the Burgers Equation, which describes the propagation of a finite-amplitude wave in a medium (Yang et al, 2014):…”

“…The intensity of the sound wave will decrease with increasing distance from the sound source (Japan Meteorological Agency, 2018). Thus, when there is an interaction of waves (l) in a medium, the number of waves must satisfy the following resonance relationship (Yang et al, 2014):…”