Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 4 / 39A / d / Solution

If a shock travels into stationary gas at speed $V$ while the downstream piston and gas travel at $V/3$, then for $\gamma=3$,
$$
\frac{\rho_1}{\rho_0}=\frac32,
\qquad
\frac{p_1}{p_0}=4,
\qquad
V=3\sqrt{\frac{p_0}{\rho_0}}.
$$


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 Incoming links: Piston-driven shock with specific-heat ratio three