It is shown that at any point P in a continuous sound field the time-averaged rate of heat generation by relaxational absorption per unit volume is given by αp02/ρc. Here p0 is the pressure amplitude at P while α is the absorption coefficient arising from relaxation when the coefficient of shear viscosity η is zero; ρ and c are, respectively, the density and velocity of sound in the medium. The result, a familiar one for plane traveling waves, is shown here to apply generally when η = 0.
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Wesley L. Nyborg (1981) studied this question.