The Cattaneo telegraph equation for temperature with moving time-harmonic source is studied on the line and the half-line domain. The Laplace and Fourier transforms are used. Expressions which show the wave fronts and elucidate the Doppler effect are obtained. Several particular cases of the considered problem including the heat conduction equation and the wave equation are investigated. The quasi-steady-state solutions are also examined for the case of non-moving time-harmonic source and time-harmonic boundary condition for temperature.
Keywords: Doppler effect; Fourier transform; Laplace transform; Telegraph equation; Time-harmonic impact; Wave equation.