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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-4/39c/b/i/solution

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Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 4 / 39C / b / i / Solution by

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

Before shock formation, the piston launches a right-moving simple wave into the undisturbed gas. The opposite invariant is fixed at its ambient value:

R_{-} = u - \frac{2 c}{γ - 1} = - \frac{2 c _{0}}{γ - 1} .

(1)

Therefore the simple-wave relation is

c = c_{0} + \frac{γ - 1}{2} u .

(2)

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