  The paper investigates a variant of semi-implicit spectral deferred
corrections (SISDC) in which the stiff, fast dynamics correspond to fast
propagating waves ("fast-wave slow-wave problem"). We show that for a scalar
test problem with two imaginary eigenvalues $i \lambda_{fast}$, $i
\lambda_{slow}$, having $\Delta t \left(\left| \lambda_{fast} \right| + \left|
\lambda_{slow} \right| \right) < 1$ is sufficient for the fast-wave slow-wave
SDC (FWSW-SDC) iteration to converge and that in the limit of infinitely fast
waves the convergence rate of the non-split version is retained. Stability
function and discrete dispersion relation are derived and show that the method
is stable for essentially arbitrary fast-wave CFL numbers as long as the slow
dynamics are resolved. The method causes little numerical diffusion and its
semi-discrete phase speed is accurate also for large wave number modes.
Performance is studied for an acoustic-advection problem and for the linearised
Boussinesq equations, describing compressible, stratified flow. FWSW-SDC is
compared to a diagonally implicit Runge-Kutta (DIRK) and IMEX Runge-Kutta
(IMEX) method and found to be competitive in terms of both accuracy and cost.
