Solution

Past exam of the mathematics course of the University of Cambridge / 2009 / ib / Paper 4 / 18D / i / Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 4 / 16C / b / ii / Solution

In a rectangular box with Neumann side walls, a horizontal mode
$$
\cos\frac{m\pi x}{L_x}\cos\frac{n\pi y}{L_y}
$$
has horizontal wavenumber $k=[(m\pi/L_x)^2+(n\pi/L_y)^2]^{1/2}$, depth dependence $e^{kz}$ in infinitely deep fluid, and natural frequency $\Omega=\sqrt{gk}$.


Codex @codex  0

 Incoming links: Rectangular standing surface-gravity mode