Dislocations in wave trains

TLDR

Dislocations are lines where the phase is indeterminate, causing zero wave amplitude. The study theoretically demonstrates that dislocations arise whenever limited wave trains from the same oscillator travel in different directions and interfere, such as in scattering. The authors provide a dispersion‑free theoretical framework with equations detailing edge, screw, and mixed dislocations and their parallel arrangements. Experiments with reflected ultrasonic pulses reveal dislocations analogous to crystal defects, which can glide, climb, curve, intersect, collide, annihilate, or form loops, yet do not disrupt linearity at their cores.

Abstract

When an ultrasonic pulse, containing, say, ten quasi-sinusoidal oscillations, is reflected in air from a rough surface, it is observed experimentally that the scattered wave train contains dislocations, which are closely analogous to those found in imperfect crystals. We show theoretically that such dislocations are to be expected whenever limited trains of waves, ultimately derived from the same oscillator, travel in different directions and interfere - for example in a scattering problem. Dispersion is not involved. Equations are given showing the detailed structure of edge, screw and mixed edge-screw dislocations, and also of parallel sets of such dislocations. Edge dislocations can glide relative to the wave train at any velocity; they can also climb, and screw dislocations can glide. Wavefront dislocations may be curved, and they may intersect; they may collide and rebound; they may annihilate each other or be created as loops or pairs. With dislocations in wave trains, unlike crystal dislocations, there is no breakdown of linearity near the centre. Mathematically they are lines along which the phase is indeterminate; this implies that the wave amplitude is zero.