A point source of oscillations on the boundary of a region

The problem of a point source of oscillations on a curve $S$ with curvature which is nowhere zero is considered:
$$ w_{tt}-w_{xx}-w_{yy}=0;\quad w|_{t<0}=0;\quad w|_s=\delta(s-s_0);\quad s,s_0\in S. $$
The case where the whispering gallery effect arises is investigated: rays issuing from a source $s_0\in S$ and reflected many times from $S$ create this effect. A function containing all singularities of $w$ is constructed explicitly. The theorem that the set of singularities of the function $w$ coincides with the wave fronts of geometrical optics is a consequence of these considerations.