The discussion centers on the relationship between the displacement curve of waves and the energy they propagate. It is established that energy is required to create displacement in waves, particularly in transverse waves, where the displacement is directly linked to the energy transmitted. The example of shaking a taut rope illustrates how energy is transferred through displacement, with energy being reflected if one end is held still. Additionally, the conversation explores the behavior of standing waves, noting that while they oscillate vertically, they do not propagate horizontally, raising questions about the connection between energy flow and displacement direction. Ultimately, the participants seek a deeper understanding of how energy influences the displacement curve in both traveling and standing waves.