Consider a normal shock wave (v perpendicular to the shock front), in which the magnetic field is parallel to the shock front, analyzed in the shock front’s rest frame.

(a) Show that the junction conditions across the shock are the vanishing of all the following quantities:

(b) Specialize to a fluid with equation of state P ∝ ρ^γ. Show that these junction conditions predict no compression, [ρ]= 0, if the upstream velocity is

For v₁ greater than this C_f, the fluid gets compressed.

(c) Explain why the result in part (b) means that the speed of sound perpendicular to the magnetic field must be C_f. C_f is the speed [Eq. (19.77)] of a fast magnetosonic wave, the only kind of sound wave that can propagate perpendicular to B.

Equation 19.77.

[pv] = [P+ pv + B / (2o)] = [h+v/2 + B/(pop)] = [vB] = 0. (19.21)