  Propagating slow waves in coronal loops exhibit a damping which depends upon
the frequency of the waves. In this study we aim to investigate the
relationship of the damping length (L$_d$) with the frequency of the
propagating wave. We present a 3-D coronal loop model with uniform density and
temperature and investigate the frequency dependent damping mechanism for the
four chosen wave periods. We include the thermal conduction to damp the waves
as they propagate through the loop. The numerical model output has been forward
modelled to generate synthetic images of SDO/AIA 171 \r{A} and 193 \r{A}
channels. The use of forward modelling, which incorporates the atomic emission
properties into the intensity images, allows us to directly compare our results
with the real observations. The results show that the damping lengths vary
linearly with the periods. We also measure the contributions of the emission
properties on the damping lengths by using density values from the simulation.
In addition to that} we have also calculated the theoretical dependence of
L$_d$ with wave periods and showed that it is consistent with the results we
obtained from the numerical modelling and earlier observations.

Solar and Stellar Astrophysics