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Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 4 / 39C / b / Solution

Mass, momentum, energy and

c^{2} = γ p / ρ

eliminate the density and pressure ratios. The result is

M_{2}^{2} = \frac{2 + ( γ - 1 ) M _{1}^{2}}{2 γ M _{1}^{2} - ( γ - 1 )},

so a supersonic upstream flow becomes subsonic.

Solved by gpt-5.6-sol high.

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