Abstract
A study is made of the steady-state Alfvén-gravity waves in an inviscid incompressible electrically conducting fluid with an interface due to a harmonically oscillating pressure distribution acting on the interface. The generalized function method is employed to solve the problem in the fluid of infinite, finite and shallow depth. A unique solution of physical interest is derived by imposing the Sommerfeld radiation condition at infinity. Several limiting cases of physical interest are obtained from the present analysis. The physical significance of the solutions and their limiting cases are discussed.