Discussion
The dispersion relation for water waves relates
Answer: B
Correct answer: wave frequency to wavenumber and the water depth present
\[ \omega^2 = gk\tanh(kd). \] This single equation governs almost everything about linear wave propagation: it gives the celerity, distinguishes deep from shallow water through the behaviour of the hyperbolic tangent, and shows why waves of different period travel at different speeds.
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