$(24-$ at atep waters and at the end of a pier located in a coastal area. The depth at the end of the pier is $15$ meters. For sake of simplicity, the engineer is only analyzing the prevailing wave for different days. The table presents the period and wave heights measured at the pier. Waves are not breaking at the end of the pier $($they behave as progressive waves$).$

$1\mathrm{.}1.$ Estimate at what depths, these waves will be sensitive to the seafloor $($i$.$e$.$ to the water depth itself$).$ Justify your results and describe the wave model and theory you are using. Hint: Use the threshold provided for deep waters $(\frac{L}{h}<mn>2</mn><mtext></mtext><mi>)</mi>$ and estimate $L($or $k=2\frac{}{L}$ with the formula in deep waters$).$ Remember that the wave period remains constant.

$1\mathrm{.}2.$ Determine phase speeds $($celerities$)$ and wave lengths for a position at deep waters and a position at the end of the pier. Hint: For the pier end, you need to know if you are in deep, intermediate or shallow waters.

$1\mathrm{.}3.$ Determine the functions for the horizontal and vertical velocities created at the surface $)=(0$ next to the pier end. Also determine the velocities at a depth of $8$ meters $(z=-8m)$ and at the seafloor $($i$.$e$.$ at depth $15m,z=-15$ m$).$ Hint: Assume a transparent pier and waves are progressive.

$1\mathrm{.}4.$ Determine the pressure function at the seafloor and next to the pier $($i$.$e$.,P$ at $z=-15$ at the pier$).$

$1\mathrm{.}5.$ The port manager would like to evaluate the amount of wave energy to deploy a power converter. The converter has a width of $50$ meters and has a height from the seafloor to the surface. What is the total energy flux arriving to the converter.