Abstract
An individual harmonic wave (i.e., having a single frequency and wavelength over all time and space) traveling in a loss-free medium has a single constant speed, which is equal to the magnitude of the phase velocity of the wave. However, when a set of different harmonic waves are traveling in the same direction, they interfere to form wave packets. In general, the peak of a wave packet travels at a speed equal to the magnitude of the group velocity that can be vastly different than the phase speeds of the component harmonic waves, even if the entire set of harmonic waves only differ among themselves slightly in frequency and wavelength. It is difficult for students to understand the origin of this difference from verbal descriptions and static graphs of wave functions at successive instants in times, such as are typically presented in textbooks. However, considerable insight is possible using the free online software Desmos.
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