Investigations are made of the wave motion which arises near resonance in a tube with an applied transverse magnetic field filled with a highly electrically conducting gas and closed by two rigid walls. The wave motion is driven by the sinusoidal radiative flux emitted by one of the walls as a consequence of its oscillatory temperature; the other wall is taken to be a perfect reflector of thermal radiation. The effects of radiative transfer are treated by the use of the differential approximation. The analysis leads to the same formal governing integral equation for the solution as arises in the ordinary gasdynamic case in the absence of electromagnetic effects. Within a narrow frequency band around resonance the theory predicts the occurrence of magnetogasdynamic shock waves which become dispersed as the thermal radiation is strengthened and may be totally dispersed to leave a continuous, periodic, but not necessarily sinusoidal, wave motion. The effect of the magnetic field is to delay the onset of dispersion.