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Improved description of shock wave evolution in media with frequency power law dependent attenuation.

A recent article by Kashcheeva et al. considers the effect of dispersion on waveform distortion and shock propagation [Acoust. Phys. 46, 170–177 (2000)]. The authors determine the dispersion from knowledge of the host material’s attenuation properties and a nearly local form of the Kramers–Kronig relations published by our laboratory in 1978. Recent work by our laboratory and others has shown that this original nearly local approximation overestimates the actual dispersion when the frequency power law describing the attenuation deviates from unity. The present letter illustrates the impact of using the exact (nonlocal) Kramers–Kronig relations on shock propagation in media with attenuation obeying a frequency power law ranging from 0–2.