A new explicit time integration scheme is presented for the solution of wave propagation problems. The method is designed to have small solution errors in the frequency range that can spatially be represented and to cut out high spurious frequencies. The proposed explicit scheme is second-order accurate for systems with and without damping, even when used with a non-diagonal damping matrix. The stability, accuracy and numerical dispersion are analyzed, and solutions to problems are given that illustrate the performance of the scheme.