Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 3 / 39A / b / Solution

Continuity of normal velocity and pressure at each density interface requires continuity of $\hat{w}$ and $d\hat{w}/dz$ at $z=\pm L$. These four conditions determine the four unknown amplitudes.

Solved by gpt-5.6-sol high.