Problem 5.207

Using the definition of the group velocity $u$, derive Rayleigh's formula (5.5d). Demonstrate that in the vicinity of $\lambda=\lambda^{\prime}$ the velocity $u$ is equal to the segment $v^{\prime}$ cut by the tangent of the curve $v$ (\lambda) at the point $\lambda^{\prime}$ (Fig. 5.36 ).