The dispersion curve shown above relates the angular frequency to the wave number k. For waves with wave numbers lying in the range k₁ < k< k₂ which of the following is true of the phase velocity and the group velocity?
A. They are in opposite directions.
B. They are in the same direction and the phase velocity is larger.
C. They are in the same direction and the group velocity is larger.
D. The phase velocity is infinite and the group velocity is finite.
E. They are the same in direction and magnitude.
(GR9277 #79)
Solution:
Phase velocity: vp = ω/k
Group velocity: vg = dω/dk
In the range k₁ < k< k₂:
vp → positive quantity
vg → negative quantity (negative slope)
→ vp and vg are in opposite directions.
Answer: A
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