Group velocity — UPSC Physics Optional CSE 2008 Paper I

Find the phase and group velocities for the wave E (z, t) = E_0 \cos (k_1 z - \omega_1 t) + \cos (k_2 z - \omega_2 t) where |k_1 - k_2| \ll k_1 k_2 ; |\omega_1 - \omega_2| \ll \omega_1, \omega_2.