An ocean bottom$-$mounted pressure sensor measures a reversing pressure

as a train of swells propagates past the sensor toward the shore. The pressure

fluctuations have a $5\mathrm{.}5s$ period and vary from a maximum of $54\mathrm{.}3k\frac{N}{m^2}$ to a

minimum of $41\mathrm{.}2k\frac{N}{m^2}.$

$($a$)$ How deep is the pressure sensor $($and bottom$)$ below the still water level?

$($b$)$ Determine the wave height, celerity, group celerity, energy, and power as it

passes the sensor$.$

$($c$)$ As a wave crest is passing the sensor determine the water particle velocity

and acceleration at a point $1\mathrm{.}5m$ above the bottom.

$50/$ Basic Coastal Engineering

$($d$)$ Calculate the deep water wave celerity, length, group celerity, energy, and

power if the wave propagates along a line perpendicular to the shore

without refracting.

$($e$)$ The nearshore bottom slope is $1$:$30.$ Calculate and plot the wave height as a

function of position from deep water into the point at which the wave breaks.