Discussion
In a waveguide the phase velocity exceeds the speed of light while the group velocity
Answer: A
Correct answer: remains below it, so no information travels faster than light
The phase velocity in a guide is \( v_p = c/\sqrt{1-(f_c/f)^2} \), which exceeds \( c \), and the group velocity is \( v_g = c\sqrt{1-(f_c/f)^2} \), which falls below it. Their product is \( c^2 \). Only the group velocity carries energy and information, so relativity is not violated - the phase velocity describes the motion of a pattern, which need carry nothing with it.
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