In the limit where a transient signal is comprised of very large frequencies, spatial regions within an inhomogeneous medium that influence the propagation from a source to a receiver lie along one or more ray paths. At lower frequencies for which the geometrical acoustic approximation is of borderline applicability, the regions that influence such transient signals are extended because of diffraction. Previous research has addressed the numerical determination of those spatial regions that influence propagation at low frequency. The present paper addresses the question of how high the center frequency need be so that the regions of influence are nearly described as ray paths for a model ocean in which the speed of sound increases nearly linearly with depth from a perfectly reflecting surface. Computations indicate that near 2500 Hz and at a range of 50 km, the region of influence resembles a ray. Noticeable departures from the ray picture are found at a range of 500 km. Various physical and mathematical causes for the departures from the ray propagation model for lower frequencies and for greater ranges are identified and discussed.