A quadratic eigenvalue problem arising in the determination of the vibratio
n modes of an acoustic fluid contained in a cavity with absorbing walls is
considered. The problem is shown to be equivalent to the spectral problem f
or a noncompact operator and a thorough spectral characterization is given.
A numerical discretization based on Raviart-Thomas finite elements is analy
zed. The method is proved to be free of spurious modes and to converge with
optimal order. Implementation issues and numerical experiments confirming
the theoretical results are reported.