According to classical acoustic theory, the Doppler shift associated with an acoustic source moving at constant velocity induces the following straining of the time coordinate:t′ =t|1‐M cos α|. Heret′ denotes the time coordinate in the fixed frame of reference (receiver),Mis the Mach number of the source, and α is the angle between the direction of motion and the direction of observation. At transonic velocitiest′ can assume a value of 0, in which case all the acoustic energy is received in an infinitesimal increment of time. This implies a transfer of infinite power so it is not physically realizable. We have used the method of characteristics to find the exact Doppler shift to a transonic source and the corresponding maximum amplitude observable at the receiver. Two cases are considered: a point source and a line source, both moving rectilinearly above a point receiver. [Work supported by the Office of Naval Research ONR.]