Kenneth D. Rolt
MIT, Dept. of Ocean Eng., Cambridge, MA 02139
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.]