A linearised hydrodynamic analysis of the density perturbations induced in a laser cavity by short, sustained and exponentially decaying discharges is described. The results obtained are compared with, and found to differ from, those of Longaker and Litvak (1969). The authors results are discussed, special emphasis being placed on those features which are characteristic of the essentially two-dimensional radial propagation of sound waves in the cavity and illustrative numerical results are presented.