Solution to 1992 Problem 79

The group velocity is defined as
\begin{align*}v_g = \frac{d \omega}{dk}\end{align*}
The phase velocity is defined as
\begin{align*}v_p = \frac{w}{k}\end{align*}
In the range k_1 < k < k_2, we can see that both \omega and k are positive, so the phase velocity is positive. On the other hand, the slope of the function \omega (k) is negative, therefore, the group velocity is negative. Therefore, answer (A) is correct.

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