  We add a time-dependent potential to the inhomogeneous wave equation and
consider the task of reconstructing this potential from measurements of the
wave field. This dynamic inverse problem becomes more involved compared to
static parameters, as, e.g. the dimensions of the parameter space do
considerably increase. We give a specifically tailored existence and uniqueness
result for the wave equation and compute the Fr\'echet derivative of the
solution operator, for which also show the tangential cone condition. These
results motivate the numerical reconstruction of the potential via successive
linearization and regularized Newton-like methods. We present several numerical
examples showing feasibility, reconstruction quality, and time efficiency of
the resulting algorithm.
