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Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 3 / 39D / b / i / Solution

In coordinates moving with the background fluid,

x^{'} = x - U t

. The stationary hill profile becomes

h = h_{0} sin (k x^{'} + k U t),

so in the convention

e^{i (k x^{'} - ω t)}

its frequency is

ω = - k U

; its physical angular frequency has magnitude

k U

.

Solved by gpt-5.6-sol high.

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