  We consider a two-dimensional analogue of Helmholtz resonator with walls of
finite thickness in the critical case when there exists an eigenfrequency
equalling to the limit of poles generated by both the bounded component of the
resonator and by the narrow connecting channel. Under assumption that the limit
eigenfrequency is simple one of the bounded component, asymptotics of two poles
converging to this eigenfrequency are constructed by using the method of
matching asymptotic expansions. The explicit formulas for the leading terms of
asymptotics for poles and for the solution of the scattering problem are
obtained.
