Radiation from an acoustic array moving at transonic velocities

Abstract

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|. Here t′ denotes the time coordinate in the fixed frame of reference (receiver), M is the Mach number of the source, and α is the angle between the direction of motion and the direction of observation. At transonic velocities t′ 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.]