  In this paper, we propose a novel high order unfitted finite element method
on Cartesian meshes for solving the acoustic wave equation with discontinuous
coefficients having complex interface geometry. The unfitted finite element
method does not require any penalty to achieve optimal convergence. We also
introduce a new explicit time discretization method for the ODE system
resulting from the spatial discretization of the wave equation. The strong
stability and optimal $hp$-version error estimates both in time and space are
established. Numerical examples confirm our theoretical results.
