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

## 2pBV3. Time domain acoustic absorption: A unified model for linear and
nonlinear acoustics.

**Kenneth D. Rolt
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*MIT, Dept. of Ocean Eng., Cambridge, MA 02139
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Dissipation of a linear acoustic wave, at frequency (omega)[sub 0], is
directly related to the pressure absorption coefficient (alpha)((omega)). In
the viscous case, (alpha)((omega))=(4/3(eta)+(eta)[sub b])(omega)[sub 0][sup
2]/(2(rho)[sub 0]c[sup 3]). For an initially (omega)[sub 0]-sinusoidal
large-amplitude nonlinear wave, the absorption coefficient is usually described
by a linear part, and by an excess part related to the harmonics from nonlinear
distortion. An alternate way to describe the absorption of a nonlinear acoustic
wave is to define a total absorption coefficient. This is done in the time
domain directly by considering dissipation in the momentum equation, and then
proceeding in an energy balance approach. The result gives the instantaneous
(alpha) for a given point on the wave in space without the need for spectral
decomposition. For the viscous case, (alpha)(x) = (4/3(eta) + (eta)[inf
b])|(cursive beta)[sup 2](nu)[inf |x[inf 0]]|/(2(rho)[inf 0]c|(nu)[inf 0]|),
where (nu) is the particle velocity and x[sub 0] is the evaluation site. For
harmonic dependence, this reduces to the preceding value (alpha)((omega)).
Similar procedures yield (alpha)(x) for heat conduction and relaxation.
Examples will be shown for the propagation of linear and nonlinear waves, in
water, and in a relaxation-type tissuelike rubber. [Work supported by C. S.
Draper Laboratory.]