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 ).