Acoustic pulse effects for media obeying a frequency power law absorption

The effects of phase velocity dispersion accompanying attenuation can alter both the shape and time delay of finite length acoustic pulses. For attenuation described by a frequency power law with an exponent y, a time causal theory [T. L. Szabo, J. Acoust. Soc. Am. 93, 2277 (A) (1993)] has shown that dispersion is greatest [in the range (0≤y≤2) when y=1 and is zero for y=0 and y=2. These results are in contrast to the approximate nearly local Kramers–Kronig theory [M. O’Donnell et al., J. Acoust. Soc. Am. 69, 696–701 (1981)] which predicts increasing dispersion as y increases from 0 to 2. The consequences of dispersion from the two theories are compared for simulated finite‐length pulses for different values of y. For values of y=1, where the theories agree, the effects of bandwidth on pulse shape and delay are illustrated. An approximate general scaling law for pulses propagating in lossy media is presented.