Acoustic field in unsteady moving media

In the interaction of an acoustic field with a moving airframe we encounter a canonical initial value problem for an acoustic field induced by an unsteady source distribution, q(t, x) with q = 0 for t = 0, in a medium moving with a uniform unsteady velocity U(t) ^i in the coordinate system x fixed on the airframe. Signals issued from a source point S in the domain of dependence D of an observation point P at time t will arrive at point P more than once corresponding to different retarded times, tau in the interval [0, t]. The number of arrivals is called the multiplicity of the point S. The multiplicity equals 1 if the velocity U remains subsonic and can be greater when U becomes supersonic. For an unsteady uniform flow U(t)^i, rules are formulated for defining the smallest number of I subdomains V_i of D with the union of V_i equal to D. Each subdomain has multiplicity 1 and a formula for the corresponding retarded time. The number of subdomains V_i with nonempty intersection is the multiplicity m of the intersection. The multiplicity is at most I. Examples demonstrating these rules are presented for media at accelerating and/or decelerating supersonic speed.