Question $6[25$ pts$.]$ Consider a hypothetical pool whose plan view is shown below. The pool uniformly shallows in the trapezoidal area $($i$.$e$.,$ ABCD $)$ until $AB,$ where water depth becomes zero. Except AB $,$ all edges of the pool are vertical walls. The trapezoidal portion of the pool area can be considered as an artificial beach, which narrows from $60$ m to $15$ m $.$ Waves of $4-$second period are generated at the deep side of the pool whose depth is $20$ m $.$ Generated waves propagate towards $AB,$ and the wave height on the deep side is $0\mathrm{.}8$ m $.$ Determine the wave height in $2-$meter$-$deep water $($Ignore the frictional losses and wave reflection due to side walls. Assume that side walls do not affect the wave fronts, that is$,$ wave crests are parallel to $AB$ and $DC.$