  This paper presents high order accurate discontinuous Galerkin (DG) methods
for wave problems on moving curved meshes with general choices of basis and
quadrature. The proposed method adopts an arbitrary Lagrangian-Eulerian (ALE)
formulation to map the acoustic wave equation from the time-dependent moving
physical domain onto a fixed reference domain. For moving curved meshes,
weighted mass matrices must be assembled and inverted at each time step when
using explicit time stepping methods. We avoid this step by utilizing an easily
invertible weight-adjusted approximation. The resulting semi-discrete
weight-adjusted DG scheme is provably energy stable up to a term which
converges to zero with the same rate as the optimal $L^2$ error estimate.
Numerical experiments using both polynomial and B-spline bases verify the high
order accuracy and energy stability of proposed methods.
