Longitudinal Magneto-Hydrodynamic Waves

The properties of longitudinal magneto-hydrodynamic waves are discussed. For a conducting fluid the presence of a strong magnetic field, on the basis of Alfven's theory, will change the sound propagation velocity. This change results from the additional forces on the conducting fluid due to the motion of the fluid in the magnetic field. The theory is extended to a fluid with finite conductivity. The case discussed deals with plane waves whose propagation direction is perpendicular to the direction of the magnetic field. It is found that the finite conductivity introduces dispersion and absorption into the propagation, which has the form of a reversed “relaxation type” frequency dependence, with the velocity decreasing with increasing frequency. The theory is applied to predict the results that would be obtained for two experiments: the propagation of sound in mercury in a very strong magnetic field; and second, the propagation of sound in sea water and the influence of the earth's magnetic field.