Past exam of the options I course of the University of Oxford / 2010 / K / K2 / Solution

For $k>0$, tryThe potential satisfies Laplace's equation, and its derivative with respect to $y$ vanishes at $y=-h$. The surface kinematic condition givesThe dynamic condition gives $-B\omega \cosh (kh)+gA=0$. Eliminating the nonzero amplitudes yieldsThus choosing either frequency sign satisfying this relation and $B=A\omega /(k\sinh (kh))$ produces the required harmonic wave.