Chapter 5.4, Problem 45E

Surfing the Perfect Wave For a wave to be surfable, it can’t break all at once. Robert Guza and Tony Bowen have shown that a wave has a surfable shoulder if it hits the shoreline at an angle $\theta$ given by

$\theta ={\sin }^{-1}\left(\frac{1}{\left(2n+1\right)\tan \beta }\right)$

where $\beta$ is the angle at which the beach slopes down and where $n=0, 1, 2,$. . . .

(a) For $\beta =10°$, find $\theta$ when $n=3.$

(b) For $\beta =15°$, find $\theta$ when $n=2, 3,$ and $4.$ Explain why the formula does not give a value for $\theta$ when $n=0$ or $1.$