  In this paper we propose and analyze a virtual element method to approximate
the natural frequencies of the acoustic eigenvalue problem with polygonal
meshes that allow the presence of small edges. With the aid of a suitable
seminorm that depends on the stabilization of the small edges method, we prove
convergence and error estimates for the eigenfrequencies and eigenfunctions of
the problem, supporting our analysis on the compact operators theory. We report
some numerical tests that allows us to assess the performance of the method and
the accuracy on the approximation.
