 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ii/paper-3/39a/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

ρ_{t}^{'} + ρ_{0} \nabla \cdot u = 0, ρ_{0} u_{t} = - \nabla p^{'}, p^{'} = c_{0}^{2} ρ^{'} .

Differentiate the first equation in time, take the divergence of the second, and use the third. This eliminates

ρ^{'}

and

u

p_{tt}^{'} = c_{0}^{2} \nabla^{2} p^{'} .

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