 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-1/40c/b/solution

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

With the convention

p = Re (p e^{iω t})

, a wave travelling in the positive

x

-direction has

p (x) = P e^{- ik x}, k = ω / c_{0} .

The linearized momentum equation gives

u = \frac{p}{ρ _{0} c _{0}}

for this right-moving wave; the sign is reversed for a left-moving wave.

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