  We introduce non conforming virtual elements to approximate the eigenvalues
and eigenfunctions of the two dimensional acoustic vibration problem. We focus
our attention on the pressure formulation of the acoustic vibration problem in
order to discretize it with a suitable non conforming virtual space for
$\mathrm{H}^1$. With the aid of the theory of non-compact operators we prove
convergence and spectral correctness of the method. To illustrate the
theoretical results, we report numerical tests on different polygonal meshes,
in order to show the accuracy of the method on the approximation of the
spectrum.

Numerical Analysis;Numerical Analysis