Here, we report a high order, high resolution coupled compact difference scheme for solving computational acoustics problems. Proposed coupled compact difference scheme displays significant spectral resolution while estimating spatial derivatives and has a physical dispersion relation preserving (DRP) ability over a wide range of wave number when a fourth order four stage Runge-Kutta scheme is used for time integration. Proposed scheme simultaneously computes the first, the second and the fourth derivative in a coupled manner at all the grid points in the domain. We have purposefully evaluated the fourth derivative term using coupled compact difference scheme to add numerical diffusion for the attenuation of unphysical spurious waves in the computed solution.