Dolphin and bat sonar: Nonlinear acoustic effects

Both dolphin and bat sonars operate in an amplitude and frequency regime where nonlinear effects can be observed, particularly distortion and the generation of harmonics. Computations illustrating these nonlinear effects are presented, quantifying effects that could be observed in experiments on echolocating signals conducted with wideband sensors. The mathematical model used is the Khokhlov-Zabolotskaya-Kuznetsov (KZK) nonlinear parabolic wave equation, which includes diffraction and absorption for directional beams, with computations performed in the time domain using a finite-difference scheme. Inputs to the computations are sample dolphin echolocation transients (clicks) and bat echolocation tone bursts (FM Chirps—fundamental component), taken from the literature for a few species of high-amplitude emitters. Calculations begin in the water or air media. Propagating high-amplitude dolphin clicks are shown to distort, create harmonics, and suffer nonlinear attenuation at ranges of tens of meters. Propagating high-amplitude bat chirps are shown capable of undergoing some nonlinear distortion at ranges within 10 m. The results may be useful in understanding the significance of nonlinear effects for work with these animals. (Work supported by ARL:UT Austin.)