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.
Solution: Using the Sommerfeld-Malyuzhinets solution, we can calculate the diffraction coefficient: $K_d = \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{\infty} e^{i k r \cos{\theta}} d \theta$. Solution: Using the dispersion relation, we can calculate
2.1 : Derive the Laplace equation for water waves. Solution: Using the dispersion relation
Solution: Using the run-up formula, we can calculate the run-up height: $R = \frac{H}{\tan{\beta}} = \frac{2}{0.1} = 20$ m. Solution: Using the dispersion relation, we can calculate
Solution: Using Snell's law, we can calculate the refraction coefficient: $K_r = \frac{\cos{\theta_1}}{\cos{\theta_2}} = \frac{\cos{30}}{\cos{45}} = 0.816$.