Problem 5.208

Find the relation between the group velocity $u$ and phase velocity $v$ for the following dispersion laws: (a) $v$ cs $1 / \sqrt{\lambda}$ (b) $v \cos k$ (c) $v \sim 1 / \omega^{2}$. Here $\lambda, k,$ and $\omega$ are the wavelength, wave number, and angular frequency.