### ASA 127th Meeting M.I.T. 1994 June 6-10

## 4pPA5. Acoustic pulse effects for media obeying a frequency power law
absorption.

**Thomas L. Szabo
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*Imaging Systems, Hewlett-Packard, 3000 Minuteman Rd., Andover, MA 01810
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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(less than or equal to)y(less than
or equal to)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.