Chapter 16, Problem 85EAP

A water wave is a shallow-water wave if the water depth d is less than $\approx \lambda /10$ . It is shown in hydrodynamics that the speed of a shall low-water wave is $v=\sqrt{gd}$ . so waves slow do as they move into shallower water. Ocean waves, with wavelengths of typically $\text{1}00\text{m}$ , are shallow-water waves when the water depth is less than $\approx \text{1}0\text{m}$ . Consider a beach where the depth increases linearly with distance from the shore until reaching a depth of 5.Om at a distance of lOOm. How long does it take a wave to move the last $\text{l00m}$ to the shore? Assume that the waves are so small that they don’t break before reaching the shore.