Question $4[10$ pts$.]$ A group of waves, propagating normal to the shore, has a wave height of $H_o$ in deep water, and the wave period is $T.$ Assuming that the wave breaking is depth$-$limited and occurs in shallow water, show that the depth at which the wave breaks $(d_b)$ is

$d_b=[\frac{g}{16}(\frac{T{H}_o^2}{{}^2}{)}^2{]}^{\frac{1}{5}}$

Note that $$ indicates the breaker index for depth$-$limited breaking and $g$ is the gravitational acceleration.