Within the framework of the assumption of large azimuthal wave numbers, the equations for Alfvén and slow magnetosonic waves are obtained using frozen-in material coordinates. These equations are specified for the case of a nonuniform magnetic field with axial symmetry. Assuming a meridional polarization of the magnetic field and velocity perturbations, the effects of Alfvén wave propagation are analyzed which are related to geometric characteristics of a nonuniform magnetic field: (a) A finite curvature radius of the magnetic field lines and (b) convergence of magnetic field lines. The interaction between the Alfvén and magnetosonic waves is found to be strongly dependent on the curvature radius of the magnetic tube and the local plasma β parameter. The electric field amplitude and the length scale of a wave front are found to increase very strongly in the course of the Alfvén wave propagation along a converging magnetic flux tube. Also studied is a temporal decrease of the wave perturbations which is caused by dissipation at the conducting boundary.