The integration of grid-forming controlled sources at a large scale is an aspect which still requires further studies and specific research. While existing literature examined stability aspects related to the integration of grid-forming converters in interconnected systems, there are only a few works dealing with disturbance propagation and wide-area damping control. Those two aspects can be addressed separately, but they also present several points of contact, which can make the research richer and more comprehensive if considered together. Concerning the first aspect, the propagation of a disturbance in case of power imbalances is strictly related to the travelling of power-frequency waves across the system. While it can be demonstrated that grid-following converters interact with the oscillations originated by the disturbance propagation just by detecting them, grid-forming converters instead interact with the power-frequency waves contributing to their propagation. For that, a conceptual revisiting of the two control strategies can be provided, introducing the definitions of grid-listening and grid-ringing terminology. Concerning the second aspect, the wide-area damping control is a well-established concept for power systems, but only recently has started to be investigated for application to grid-forming converters as local actuators. The flexibility provided by the grid-forming synchronization loop offers the opportunity for the formulation of advanced control strategies, based on external control signals which are possibly provided by wide-area control architectures. The involvement of grid-forming converters as actuators can lead to a significant improvement in the dynamic performance of the power system, ultimately modifying their reaction with respect to the oscillations due to the propagation of a disturbance in the system. The work aims therefore at addressing those two aspects with a unified and comprehensive approach. The study on disturbance propagation and wide-area damping control is first introduced from a theoretical point of view, then numerical simulations and examples are presented. The results are obtained with phasor RMS simulations, which have been proved to be suitable for grid-forming converters when investigating slow dynamics in power systems. The work provides a deeper understanding about the travelling dynamics of power-frequency waves across power systems with grid-forming converters, discussing the conceptual relationship and opportunity of wide-area damping control, for a coordinated synchronization among several grid-forming sources operating in the system at a large scale.