Surface stability of a magnetized liquid covered with a thin elastic film

The linear waves on the flat horizontal interface between two magnetized liquids, which are covered with a weightless nonmagnetic elastic film, are investigated. The liquids are situated in a uniform magnetic field H of an arbitrary orientation and in the gravitational field g. An example is given using the equation of motion for free elastic film where the solutions are substituted into the equation yielding a dispersion equation for the waves. It is concluded that the dispersion equation determines the resonance frequency when the waves, on the surface of the liquid, are excited by a running or stationary magnetic field.