  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 discretisation and a stochastic trigonometric scheme for the
temporal approximation. This explicit time integrator allows for error bounds
independent of the space discretisation and thus do not have a step size
restriction as in the often used St\"ormer-Verlet-leap-frog scheme. Moreover it
enjoys a trace formula as does the exact solution of our problem. These
favourable properties are demonstrated with numerical experiments.
