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.