Surface tension — UPSC Physics Optional CSE 1991 Paper I

The phase velocity of surface waves of wavelength \lambda is v_p = \left( \frac{2 \pi T}{\lambda \rho} + \frac{g \lambda^{1/2}}{2 \pi} \right) where T is the surface tension and \rho the density of the liquid and g is acceleration due to gravity. Find the group velocity and express it in terms of the phase velocity. For which wavelength is the phase velocity a minimum ?