Phase velocity refers to the speed at which a wave phase propagates in space, calculated as the ratio of angular frequency (ω) to wave number (κ). In contrast, group velocity represents the speed at which the overall envelope of a wave packet or group of waves travels, determined by the derivative of angular frequency with respect to wave number (dω/dκ). The key distinction lies in their physical interpretations: phase velocity applies to individual wave components, while group velocity pertains to the collective behavior of wave packets. Understanding this difference is crucial for analyzing wave phenomena in various fields, including physics and engineering. The discussion concludes with acknowledgment of helpful animations that clarify these concepts.
