The description of anharmonic properties of solids, such as thermal expansion or the interaction of thermal and acoustic phonons, involves generalized Grüneisen parameters that describe the strain dependence of the lattice vibrational frequencies. In the Debye model of specific heats the lattice vibrations are approximated by long wavelength acoustic standing-wave modes of a dispersionless elastic continuum in which the generalized Grüneisen parameters are frequency independent. Recently, a new ultrasonic measurement technique has been developed which uses such long wavelength acoustic modes to monitor axially induced accumulated static loads in threaded fasteners from a state of zero initial stress. A fundamental calibration parameter of the new technique is the stress acoustic constant defined as the fractional change in the resonant standing-wave frequency in the solid cavity per unit applied axial stress. We generalize the equations of elastic wave motion and their solutions to include nonzero homogeneous initial stresses and redefine the stress acoustic constants to include the effect of initial stress. The relationship between the newly defined stress acoustic constants and the strain-generalized Grüneisen parameters is derived, and the implications to material anharmonicity and nonlinear thermoelasticity discussed.
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