In this paper we study the generation and propagation of hydromagnetic waves during the spin-up of an electrically conducting, viscous fluid. The time-dependent motion is set up by the impulsive rotation of an infinitely conducting plane which is initially in rigid-body rotation with the fluid, the applied magnetic field being parallel to the axis of rotation. The hydromagnetic flow is permeated by two distinct wave modes and the region between their wave fronts supports harmonic waves produced by the inertial oscillations. The characteristics of these modes are discussed for some limiting cases of interest.