Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 1 / 40C / b / Solution

With the convention $\tilde{p}=\mathrm{Re}(\hat{p}{e}^{i\omega t})$, a wave travelling in the positive $x$-direction hasThe linearized momentum equation givesfor this right-moving wave; the sign is reversed for a left-moving wave.

Solved by gpt-5.6-sol high.