Examples covering deep water and shallow water approximations, dispersion relationships, and wave transformation.

A deep-water offshore wave has a recorded period ($T$) of 10.0 seconds.

A wave approaches the coastline and enters an area where the water depth ($d$) is only 4.0 meters. Calculate the phase speed (celerity) of this shallow water wave.

An offshore wave with a deep water wave height ($H_0$) of 3.5 meters approaches a harbor entrance. The local wave transformation coefficients are: Shoaling coefficient ($K_s = 1.15$), Refraction coefficient ($K_r = 0.95$), and Diffraction coefficient ($K_d = 0.85$) due to a nearby headland. Calculate the local wave height ($H$) entering the harbor.

A wave with a period ($T$) of 8.0 seconds travels through intermediate water with a depth ($d$) of 15.0 meters. The required hyperbolic tangent value for this specific condition is $\tanh(0.97) \approx 0.748$. Determine the wavelength ($L$).