Solution

Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 3 / 39B / i / Solution

{title2=$\omega^2=(T/\rho)|k|^3$}

For a capillary wave on deep water with surface tension $T$ and density $\rho$, the dispersion relation is
$$
\omega(k)=S|k|^{3/2},
\qquad
S=\sqrt{T/\rho}.
$$
Its group velocity is $(3S/2)|k|^{1/2}$ in the direction of the wavevector.


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 Incoming links: Deep-water capillary-wave dispersion relation