For the fast and slow MHD waves, let u and u t denote the components of

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For the fast and slow MHD waves, let u and ut denote the components of the mass flow velocity that are longitudinal and transverse, respectively, to the direction of propagation. Show that u and ut are in phase for the fast wave and 180° out of phase for the slow wave. Also, show that the perturbations in the kinetic and magnetic pressures are in phase for the fast wave and 180° out of phase for the slow wave.

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