The linear theory of thermoelasticity without energy dissipation for homogeneous and isotropic materials is employed to study one-dimensional waves in a half-space. The waves are supposed to be due to sudden inputs of temperature and stress/strain on the boundary. The Laplace transform method is employed to solve the problem. Exact solutions, in closed form, for the displacement, temperature, strain, and stress fields are obtained. The characteristic features of the underlying theory are analyzed in light of these solutions and their counterparts in earlier works.