We apply the discontinuous Petrov-Galerkin (DPG) method to linear acoustic waves in space and time using the framework of first-order Friedrichs systems. Based on results for operators and semigroups of hyperbolic systems, we show that the ideal DPG method is wellposed. The main task is to avoid the explicit use of traces, which are difficult to define in Hilbert spaces with respect to the graph norm of the space-time differential operator. Then, the practical DPG method is analyzed by constructing a Fortin operator numerically. For our numerical experiments we introduce a simplified DPG method with discontinuous ansatz functions on the faces of the space-time skeleton, where the error is bounded by an equivalent conforming DPG method. Examples for a plane wave configuration confirms the numerical analysis, and the computation of a diffraction pattern illustrates a first step to applications.