The group velocity of a wave packet is defined by the formula v_g = dω/dk, where the wave number k influences the velocity. The discussion highlights the complexity of interpreting this relationship, particularly when ω and k are not linearly related, leading to varying slopes in the group velocity. It is noted that while different points in the wave packet travel at different velocities, the wave number is typically associated with the entire packet rather than individual segments. Suggestions for determining the wave number include using the average wavelength or analyzing the frequency spectrum of the wave packet. The conversation emphasizes the challenges posed by dispersion, which causes the wave packet to lose its shape and complicates the selection of an appropriate wave number.
