“Whispering” waves and Bate’s ridges in numerical experiments

Abstract

The whispering-gallery effect can be simulated using wave front constructions on rays. Results show that sources placed close to the boundary of an elliptic domain will exhibit the whispering-gallery effect. It illustrates that the energy of wave fronts close to boundaries remains dense. The wave fronts form patterns of repeated ridges which are related to the experimental observations of sharp ridges by Bate. The energy of the wave fronts does not remain dense near the boundary for all convex domains. This fact is illustrated using the stadium billiard, where the Bate’s ridges spread when leaving the curved area.