  In this paper we analyze a finite element method for solving a quadratic
eigenvalue problem derived from the acoustic vibration problem for a
heterogeneous dissipative fluid. The problem is shown to be equivalent to the
spectral problem for a noncompact operator and athorough spectral
characterization is given. The numerical discretization of the problem is based
on Raviart-Thomas finite elements. The method is proved to be free of spurious
modes and to converge with optimal order. Finally, we report numerical tests
which allow us to assess the performance of the method.
