4.2 : A wave is diffracted around a semi-infinite breakwater. What is the diffraction coefficient?
2.1 : Derive the Laplace equation for water waves.
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.