An inequality for longitudinal and transverse wave attenuation coefficients.

Total absorption, defined as the net flux of energy out of a bounded region averaged over one cycle for time harmonic motion, must be non-negative when there are no sources of energy within the region. This passivity condition places constraints on the non-dimensional absorption coefficients of longitudinal and transverse waves, γL and γT, in isotropic linearly viscoelastic materials. Typically, γL, γT are small, in which case the constraints imply that coefficients of attenuation per unit length, αL, αT, must satisfy the inequality αL/αT≥4cT3/3cL3 where cL, cT are the wave speeds. This inequality, which as far as the author is aware, has not been presented before, provides a relative bound on wave speed in terms of attenuation, or vice versa. It also serves as a check on the consistency of ultrasonic measurements from the literature, with most but not all of the data considered passing the positive absorption test.