x})=e^{-i\omega
t}u({\textbf x})$$ the wave equation (\[2-1\]) is reduced to the Helmholtz equation $$\label{2-3}
(\Delta +k^2)\,
 u(\textbf{x}) =0, \quad
k={\omega}/{c}\,{.}$$

The oscillations in the internal region $D_{\text{in}}$ are described by an infinite countable set of normal modes $$\label{2-4}
u_n(t,\textbf{x})=e^{-i\omega _n t}u_n(\textbf{x}), \quad
n=1,2,\ldots .$$ The spatial form of the normal modes (the functions $u_n(\textbf{x})$) is determined by the boundary conditions which are imposed upon the function $u(\textbf{x})$ on the internal side of the surface $S$. These conditions should fit the physical content of the problem under study. The set of normal modes is a complete one. Hence any solution of (\[2-3\]) obeying relevant boundary conditions can be expanded in terms of the normal modes $u_n(\textbf{x})$.

When considering the oscillations in the external domain $D_{\rm
ex }$ one imposes, in addition to the conditions on the compact surface $S$, a special requirement concerning the behavior of the function $u(\textbf{x})$ at large $r\equiv |\textbf{x}|$. In the classical mathematical physics [@RR] the radiation conditions, proposed by Sommerfeld [@Sommerfeld; @FM], are used here $$\label{2-5} \lim_{r\to \infty} r^{\frac{d-1}{2}}u(r)=
\textrm{const}\,{,}\qquad  \lim_{r\to\infty}r^{\frac{d-1}{2}}\left
( \frac{\partial u}{\partial r} -i ku\right )= 0\,{.}$$ For real values of the wave vector $k$ (for real frequencies $\omega$) the solution to Eq. (\[2-3\]), 