Recently, a closed time-reversal cavity for electromagnetic waves was demonstrated and experimentally realized using a network of transmission lines. This paper presents an analysis in the frequency domain of the wave propagation characteristics that pertain to the time-reversal cavity. The study illustrates, in the frequency domain, that the backward-propagation wave consists of the converging and diverging components, and only the converging wave constitutes a time-reversed counterpart of the forward-propagation wave. Moreover, it is found that the interfering effect of the diverging wave can exist for any of the observation points along the transmission line network. Finally, the analysis demonstrates that an active time-reversal sink remains effective in the frequency domain to overcome the interfering effect.