The acoustic conservation equations are a subset of the compressible flow equations and describe the generation and propagation of acoustic waves by the two acoustic primary variables: acoustic pressure and acoustic particle velocity. Therefore, the equations (an exact reformulation of the APE-2) can be natively used in the context of hybrid aero-acoustic. In order to achieve a stable finite element (FE) approximation, these two physical quantities have to be defined in different Sobolev spaces to fulfill the Ladyzhenskaya-Babuska-Brezzi condition. We choose the second possibility, i.e., the Discontinuous Galerkin (DG) method, which enforces coupling between elements via numerical fluxes in surface integrals only and thus has advantages regarding computational efficiency. We present a high-order formulation in space and time that yields optimal convergence rates and provide implementation details in the context of hybrid aero-acoustics. Furthermore, the application to practical aero-acoustic cases will demonstrate the developed DG approach high accuracy and high computational efficiency.