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Pressure in a perfect-gas simple wave

In a right-moving simple wave entering gas initially at rest with sound speed

c_{0}

, the other Riemann invariant is constant, so

c = c_{0} + \frac{γ - 1}{2} u .

The isentropic relation

\frac{p}{p _{0}} = (\frac{c}{c _{0}})^{2 γ / (γ - 1)}

converts the velocity disturbance into its nonlinear pressure disturbance.

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