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 α L / α T ≥ 4 c T 3 / 3 c L 3 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.