Phase Changes and Pulse Deformation in Acoustics

Abstract

Acoustic waves generated by a point source in the ocean or atmosphere may be reflected due to total internal reflection by regions of increasing sound velocity- i.e., by the bending back of ray paths at turning points. This phenomenon is usually accompanied by the simultaneous formation of caustics. The relationship between caustics and turning point effects can be explored by the use of WKB and stationary phase approximations for the case of a harmonic point source in a homogeneous fluid overlying a stratified section. If one examines the behavior of reflected waves traveling along a given ray path, one sees that the conditions for formation of a caustic in the stratified section and for a −π/2 phase shift occurring within this section are identical. If, on the other hand, the point source is removed to infinity, one recovers the plane-wave case: The caustic becomes the horizontal turning-point plane and the −π/2 phase shift becomes a turning-point effect. These features are reviewed; and it is concluded that, in stratified media, the −π/2 phase shift due to a turning point is simply the plane-wave limit of the caustic effect, a limit that is approached asymptotically when the source is removed to great distances.