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

Forward Modelling of Propagating Slow Waves in Coronal Loops and Their Frequency-Dependent Damping