The present paper is aimed at studying the effects of viscosity and time on the propagation of thermoelastic waves in a homogeneous and isotropic three-dimensional medium whose surface is acted upon by a thermal load under the purview of temperature-rate-dependent thermoelasticity. The normal mode analysis technique has been employed to solve the resulting non-dimensional coupled field equations and hence the exact expressions for displacement component, stress, temperature field and strain are obtained. The problem is further illustrated by computing the numerical values of the field variables for a copper- like material and depicting them graphically. Numerical results predict finite speed of propagation for thermoelastic waves.
