\documentclass[12pt,leqno,A4]{article} \begin{document} Modeling of plane harmonic waves in a microperiodic layered infinite thermoelastic solid via an eight-order in time partial differential equation involving a high intrinsic mechanical frequency $\Omega_M$ and a high intrinsic thermal frequency $\Omega_T$ was proposed by the present author before [see J. Ignaczak, Proceedings TS2003, TS2003, June 8-11, 2003, Blacksburg, VA, U.S.A.]. It was shown there that there are two harmonic waves of a given frequency $\omega $ propagating in a positive direction normal to the layering when $\Omega_M \rightarrow \infty $ and $\Omega_T < \infty,$ or $\Omega_M < \infty $ and $\Omega_T \rightarrow \infty.$ In the present paper the existence of two dispersive and attenuated harmonic waves of a given frequency $\omega $ is proved when $\Omega_M < \infty $ and $\Omega_T < \infty .$ Also, a closed-form of the associated velocities and attenuation coefficients is obtained. Numerical results illustrating the two waves for a particular composition of the microperiodic layered thermoelastic solid are included. \end{document}