ACOUSTIC FIELD IN UNSTEADY MOVING-MEDIA

In the interaction of an acoustic field with a moving airframe, a cano nical initial value problem for an acoustic field induced by an unstea dy source distribution q(t,x) with q=0 for t less than or equal to 0, in a medium moving with a uniform unsteady velocity U(t)<(iota)over ca p> in the coordinate system x fixed on the airframe, is encountered. S ignals issued from a source point S in the domain of dependence D of a n 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]. T he number of arrivals is called the multiplicity of the point S. The m ultiplicity equals one if the velocity U remains subsonic and can be g reater when U becomes supersonic. For an unsteady uniform flow U(t)<(i ota)over cap>, rules are formulated for defining the smallest number o f I subdomains V-i of D with the union of V-i equal to D. Each subdoma in has multiplicity 1 and a formula for the corresponding retarded tim e. The number of subdomains V-i with nonempty intersection is the mult iplicity m of the intersection. The multiplicity is at most I. Example s demonstrating these rules are presented for media at accelerating an d/or decelerating supersonic speed.