A pressure sensor$,$ mounted at $1m$ above the sea bottom, measures the pressure reading $($due to a wave$)$ that varies from a maximum of $54\mathrm{.}3k\frac{N}{m^2}$ to a minimum of $41\mathrm{.}2k\frac{N}{m^2}.$

The time difference between the occurrence of maximum and minimum pressure readings is $3\mathrm{.}5$ seconds.

$($a$)$ How deep is the sea bottom below the still water level?

$($b$)$ Determine the wave length and wave height.

$3\%$

$8\%$

$($c$)$ Calculate the deep$-$water wave celerity and wave length if the wave propagates along a line perpendicular to the shore without refracting.

$($d$)$ At what depth this wave would break?

$5\%$

$4\%$