On the adequacy of linear acoustics for prediction of acoustic pressure transients created by laser beams moving over water surfaces at sonic speeds

Abstract

Previous discussions of laser‐generated sound, particularly with reference to themoacoustic effects, are often based on linear equations. However, seemingly plausible arguments can be developed to the effect that the peak acoustic pressure predicted by a linear theory will grow without bound when the sound is generated by a laser beam that travels for an indefinitely long period of time over a water surface at exactly the speed of sound. One consequently asks (1) whether the linear model does indeed predict a pressure singularity for a sonically moving laser beam, and (2) whether nonlinear effects can be neglected. Analysis by two different methods (Fourier transforms and method of retarded potentials using the transient (Green's function) shows that the linear acoustic framework does not predict any singularity in the acoustic pressure generated by a thermoacoustic source moving at the speed of sound over a water surface. Additional theoretical considerations strongly suggest that cumulative nonlinear effects can be ignored during the buildup phase of the acoustic pulse. The key ingredient in the mathematical model, which holds the peak pressure to a finite value, is the pressure release boundary condition at the water surface. However, once the acoustic pulse is launched (i.e., after the laser is turned off), accumulative nonlinear steepening effects may alter the received pressure waveform. In the latter case, a quasi‐one‐dimensional nonlinear acoustics model based on Burger's equation is expected to be adequate to predict the nonlinear distortion in farfield sound propagation. [Work supported by ONR.]