  The infinitesimal generator (fractional Laplacian) of a process obtained by
subordinating a killed Brownian motion catches the power-law attenuation of
wave propagation. This paper studies the numerical schemes for the stochastic
wave equation with fractional Laplacian as the space operator, the noise term
of which is an infinite dimensional Brownian motion or fractional Brownian
motion (fBm). Firstly, we establish the regularity of the mild solution of the
stochastic fractional wave equation. Then a spectral Galerkin method is used
for the approximation in space, and the space convergence rate is improved by
postprocessing the infinite dimensional Gaussian noise. In the temporal
direction, when the time derivative of the mild solution is bounded in the
sense of mean-squared $L^p$-norm, we propose a modified stochastic
trigonometric method, getting a higher strong convergence rate than the
existing results, i.e., the time convergence rate is bigger than $1$.
Particularly, for time discretization, the provided method can achieve an order
of $2$ at the expenses of requiring some extra regularity to the mild solution.
The theoretical error estimates are confirmed by numerical experiments.
