© 1976 by Oxford University Press
GRAVITY MODIFIED SOUND WAVES IN A CONDUCTING STRATIFIED ATMOSPHERE
( School of Mathematics, University of Newcastle upon Tyne )
Vertically propagating sound waves in a perfectly conducting horizontally stratified atmosphere in the presence of a uniform horizontal magnetic field are analysed. The study depends on the assumption that variations in the particle speed, magnetic field, and particle density are small so that the equations of motion, continuity, and magnetic induction may be linearized. Assuming a harmonic time variation for the magneto-acoustic waves, the particle speed satisfies a second-order differential equation which may be expressed in hypergeometric form. Approximate analytic solutions are obtained for the magnetic field of the waves, the particle speed and number-density variation; formal solutions are also given. Under certain circumstances, a standing wave solution is obtained for which the magnetic field decreases directly as the particle density 
(for wave frequencies over a certain critical value); Hankel asymptotic expansions yield a wave with magnetic field varying as 
under different parameter restrictions, and a harmonic progressive wave, with amplitude increasing exponentially with distance, is also obtained for a certain frequency range.