4.1 : A wave with a wavelength of 50 m is incident on a vertical wall. What is the reflection coefficient?
Solution: Using the dispersion relation, we can calculate the wave speed: $c = \sqrt{\frac{g \lambda}{2 \pi} \tanh{\frac{2 \pi d}{\lambda}}} = \sqrt{\frac{9.81 \times 100}{2 \pi} \tanh{\frac{2 \pi \times 10}{100}}} = 9.85$ m/s.
5.2 : A wave with a wave height of 2 m and a wavelength of 50 m is running up on a beach with a slope of 1:10. What is the run-up height?