Dispersion relation — UPSC Physics Optional CSE 1990 Paper I

For a certain wave, system the angular velocity \omega and the wave vector k are related as follows: \omega = \omega_0 \left| \sin \frac{k a}{2} \right| \quad \text{for } -\frac{\pi}{a} < k < \frac{\pi}{a} Determine and plot the phase velocity and the group velocity for this system.