 Solution

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

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

For a progressive plane wave, write

p^{'} = P e^{i (k \cdot x - ω t)}, u = U k e^{i (k \cdot x - ω t)} .

ρ_{0} ω U = k P

ω = c_{0} k

. Therefore the pressure and longitudinal velocity amplitudes obey

\frac{P}{U} = ρ_{0} c_{0} =: Z .

The constant

Z

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