Waves inside a concave cylindrical surface and whispering gallery

Some of the waves inside a concave cylindrical surface are dealt with in this paper. Particular attention is paid to the acoustic whispering gallery phenomena. The closely bound whispering gallery mode decreases in the direction perpendicular to the circumferential direction for a point source. Expressions for reflected waves from the concave surface and the graphic method for determination of caustic are given in the case of line source excitation.