  In the present paper we describe a method for solving inverse problems for
the Helmholtz equation in radially-symmetric domains given multi-frequency
data. Our approach is based on the construction of suitable trace formulas
which relate the impedance of the total field at multiple frequencies to
derivatives of the potential. Using this trace formula we obtain a system of
coupled differential equations which can be solved to obtain the potential in a
stable manner. Finally, the performance of the reconstruction algorithm is
illustrated with several numerical examples.
