Green's function of a pulse sound source in a uniform subsonic flow

Subject and Purpose. The wave field produced by a spatial-temporal distribution of sound sources in a uniform subsonic flow is theoretically studied in an effort to obtain an analytical dependence of the sound field on physical parameters.

Method and Methodology. Cauchy problem for wave equation in a moving medium is solved using a spatial-waveguide Fourier expansion of the sound field. A Fourier representation of the Green's function of a point-like pulse sound source is constructed whose inverse transform allows us to obtain the Green's function spatial-temporary representation. 

Results. With the Green’s function obtained, the wave fields from arbitrarily shaped sources have been represented in the “wave potential” form, which is a convolution type integral of the density of spatial-temporal distribution of the sound sources and the Green’s function.

Conclusion. The calculation results give a clear idea of the propagation of sound waves excited by a point-like pulse source in a uniform homogeneous flow. The wave front of the sound field represents a sphere whose center “drifts” from the source at a speed equal to the speed of the flow in its movement direction, and the radius of the sphere grows in the course of time at a speed equal to the speed of sound. The obtained Green’s function allows for the analytic continuation to the supersonic flow case that, in contrast to the subsonic case, satisfies the causality principle not in all unlimited space but only at the observation points within the Mach cone.

The wave field from a monochromatic source is the limiting case of the rectangular pulse solution.