Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 314 / 3 / a

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Solution

The adiabatic sound speed and Alfvén speed are

v_{s}^{2} = (\frac{\partial p}{\partial ρ})_{s} = \frac{γ p}{ρ}, v_{A} = \frac{B}{μ _{0} ρ}, v_{A} = \frac{B}{μ _{0} ρ} .

The entropy is held fixed in the sound-speed derivative.

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