  Chromospheric inferences rely on the interpretation of spectral lines that
are formed under Non-Local Thermodynamic Equilibrium (NLTE) conditions. In the
presence of oscillations, changes in the opacity impact the response height of
the spectral lines and hinder the determination of the real properties of the
fluctuations. We aim to explore the relationship between the chromospheric
oscillations inferred by NLTE inversion codes and the waves' intrinsic
fluctuations in velocity and temperature. Numerical simulations of wave
propagation in an umbra have been computed with the code MANCHA. The NLTE
synthesis and inversion code NICOLE has been used to compute
spectropolarimetric Ca II 8542 \AA\ line profiles for the models obtained from
the simulations. The synthetic profiles have been inverted and the inferences
from the inversions have been compared with the known simulated atmospheres.
NLTE inversions of the Ca II 8542 \AA\ line capture low-frequency oscillations,
including those in the main band of chromospheric oscillations around 6 mHz. In
contrast, waves with frequencies above 9 mHz are poorly characterized. Velocity
oscillations at those higher frequencies exhibit clear indications of opacity
fluctuations. The main response of the line to velocity fluctuations comes from
low chromospheric heights, whereas the response to temperature shows sudden
jumps between the high photosphere and the low chromosphere. This strong
variation in the heights where the line is sensitive to temperature is revealed
as a strong oscillatory power in the inferred fluctuations. Our results
validate the use of NLTE inversions to study chromospheric oscillations with
frequencies below 9 mHz. The interpretation of higher frequency oscillations
and the power of temperature oscillations must be addressed with care since
they exhibit signatures of opacity oscillations.
