Problem $2(25$ points$)$

Given: The dispersion relationship: ${}^2=$kgtanh$(kd)$

Consider the following wave properties:

a$)T=7\mathrm{.}3sec,$ Deep Water

b$)T=7\mathrm{.}3sec,$ Water depth $=3\mathrm{.}1m($intermediate depth$)$

c$)T=7\mathrm{.}3sec,$ Water depth $=1\mathrm{.}2m($Shallow depth$)$

Required:

a$)(15$ points$)$ Using the dispersion relationship, determine the associated wavelength for

a$)-$ c$)$ above.

b$)(5$ points$)$ What is the minimum water depth for this wave to be considered a

deepwater wave?

c$)(5$ points$)$ How would increasing the wave period to $T=14\mathrm{.}1sec$ influence the water

depth to be classified as a deep water wave? Would the depth need to be higher or

lower? How do you think this would influence the shallow and intermediate water

depth specifications?