  Stokes inversion codes are crucial in returning properties of the solar
atmosphere, such as temperature and magnetic field strength. However, the
success of such algorithms to return reliable values can be hindered by the
presence of oscillatory phenomena within magnetic wave guides. Returning
accurate parameters is crucial to both magnetohydrodynamics studies and solar
physics in general. Here, we employ a simulation featuring propagating MHD
waves within a flux tube with a known driver and atmospheric parameters. We
invert the Stokes profiles for the 6301 $\unicode{0xc5}$ and 6302
$\unicode{0xc5}$ line pair emergent from the simulations using the well-known
Stokes Inversions from Response functions (SIR) code to see if the atmospheric
parameters can be returned for typical spatial resolutions at ground-based
observatories. The inversions return synthetic spectra comparable to the
original input spectra, even with asymmetries introduced in the spectra from
wave propagation in the atmosphere. The output models from the inversions match
closely to the simulations in temperature, line-of-sight magnetic field and
line-of-sight velocity within typical formation heights of the inverted lines.
Deviations from the simulations are seen away from these height regions. The
inversion results are less accurate during passage of the waves within the line
formation region. The original wave period could be recovered from the
atmosphere output by the inversions, with empirical mode decomposition
performing better than the wavelet approach in this task.
