 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-4/39a/b/solution

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

Insert

h = γ p / [ρ (γ - 1)]

, eliminate

p_{2}

and the downstream normal speed using mass conservation, and solve for the density ratio. This gives

\frac{ρ _{1}}{ρ _{2}} = \frac{2 c _{1}^{2} + ( γ - 1 ) U ^{2}}{( γ + 1 ) U ^{2}}, c_{1}^{2} = \frac{γ p _{1}}{ρ _{1}} .

 New to topics? Read the docs here!