Slowing and stopping the speed of sound

Abstract

Temporal interference between direct and surface-reflected paths induces large variation in the group speed of an acoustic signal between a source and receiver. This speed goes to zero when the source and receiver approach one another and are within $c \tilde{\delta t}/2$ of the surface, where $c$ is the in-situ speed of sound and $\tilde{\delta t}$ is the smallest temporal separation between the paths at which interference initiates. At greater depths, the group speed can drop by many orders of magnitude. The effect diminishes far from a receiver as the size of the delay shrinks relative the overall time of propagation. The phenomenon is of great importance for methods designed to locate sounds via time differences of arrival (TDOA) as the group speed between a sound and each receiver may differ by orders of magnitude, a phenomenon that invalidates the geometrical interpretation of location by hyperboloids. Isodiachronic geometries are required to derive valid locations. Analogous to gravitational black holes, where the speed of light is zero at the event horizon, ``three-dimensional acoustical black holes'' an be present at acoustical receivers.