Q5Electromagnetics Waves
Question
Q.5 Explain the term group velocity.
Answer
Group velocity vg = dω/dβ is the speed at which the envelope of a modulated wave packet (and hence energy/information) actually travels through a dispersive medium or waveguide, generally different from the phase velocity vp = ω/β.
Group velocity is defined as the rate of change of angular frequency with respect to phase constant:
Physically, when a signal is a superposition of many closely spaced frequency components (a modulated wave packet, as any real information-carrying signal must be, since a pure single-frequency sinusoid carries no information), the observable envelope of that packet moves at the group velocity, while the individual phase fronts within the envelope move at the (possibly different) phase velocity. In a non-dispersive medium (vp independent of frequency, e.g. free space or an ideal lossless dielectric), vg = vp exactly; in any dispersive medium — including a waveguide (where vg = c²/vp < c always) or a lossy conducting medium — vg and vp differ, and it is specifically vg, not vp, that is constrained to remain at or below the speed of light c by relativistic causality, since vg is the velocity that actually carries energy and information.