 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-3/39d/b/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

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)}

ω = - k U

; its physical angular frequency has magnitude

k U

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