  In this paper, we develop a provably energy stable and conservative
discontinuous spectral element method for the shifted wave equation in second
order form. The proposed method combines the advantages and central ideas of
very successful numerical techniques, the summation-by-parts finite difference
method, the spectral method and the discontinuous Galerkin method. We prove
energy-stability, discrete conservation principle, and derive error estimates
in the energy norm for the (1+1)-dimensions shifted wave equation in second
order form. The energy-stability results, discrete conservation principle, and
the error estimates generalise to multiple dimensions using tensor products of
quadrilateral and hexahedral elements. Numerical experiments, in
(1+1)-dimensions and (2+1)-dimensions, verify the theoretical results and
demonstrate optimal convergence of $L^2$ numerical errors at subsonic, sonic
and supersonic regimes.
