  Studies based on high-resolution spectroscopic data of rapidly oscillating Ap
stars show a surprising diversity of pulsation behavior in the atmospheric
layers, pointing, in particular, to the co-existence of running and standing
waves. The correct interpretation of these data requires a careful modelling of
pulsations in these magnetic stars. In light of this, in this work we present a
theoretical analysis of pulsations in roAp stars, taking into account the
direct influence of the magnetic field. We derive approximate analytical
solutions for the displacement components parallel and perpendicular to the
direction of the magnetic field, that are appropriate to the outermost layer.
From these, we determine the expression for the theoretical radial velocity for
an observer at a general position, and compute the corresponding pulsation
amplitude and phase as function of height in the atmosphere. We show that the
integral for the radial velocity has contributions from three different types
of wave solutions, namely, running waves, evanescent waves, and standing waves
of nearly constant amplitude. We then consider a number of case studies to
illustrate the origin of the different pulsational behaviour that is found in
the observations. Concerning pulsation amplitude, we find that it generally
increases with atmospheric height. Pulsation phase, however, shows a diversity
of behaviours, including phases that are constant, increasing, or decreasing
with atmospheric height. Finally, we show that there are situations in which
the pulsation amplitude goes through a zero, accompanied by a phase jumps of
$\pi$, and argue that such behaviour does not correspond to a pulsation node in
the outermost layers of the star, but rather to a visual effect, resulting from
the observers inability to resolve the stellar surface.
