A fully discrete approximation of the linear stochastic wave equation driven by additive noise is presented. A standard finite element method is used for the spatial discretization and a stochastic trigonometric scheme for the temporal approximation. This explicit time integrator allows for error bounds independent of the space discretization and thus does not have a step-size restriction as in the often used Störmer--Verlet-leap-frog scheme. Moreover, it enjoys a trace formula as does the exact solution of our problem. These favorable properties are demonstrated with numerical experiments.
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