Investigation of the Shadow Zone for a Particular Sound Velocity Variation

Abstract

In a previous paper [J. Acoust. Soc. Am. 30, 684(A) (1958)] an exact solution was presented for wave propagation in an inhomogeneous medium characterized by a sound velocity variation, c = c0z/(z2−a2)12, for a point source at z0, z0>a. In this paper specific properties of this solution are investigated for real values of a. In this case a shadow zone is produced with a caustic as a boundary. It is shown that the above solution is greatly simplified for a coordinate system in which the caustic is a coordinate line. A general expression for the sound intensity is derived and numerical results for regions on both sides are presented. Frequency as a parameter is discussed and a comparison is made with the results derived by Brekhovskikh [Soviet Phys.-Acoustics 2, 124 (1956)] in the high-frequency limit for regions about the caustic. (This work was supported by the Bureau of Ordnance, U. S. Navy, under Contract NOrd 12937.)