The profiles of an acoustic field and electric potential of the forward and backward shear-horizontal (SH) acoustic waves of a higher order propagating in X-Y potassium niobate plate have been theoretically investigated. It has been shown that by changing electrical boundary conditions on a surface of piezoelectric plates, it is possible to change the distributions of an acoustic field and electric potential of the forward and backward acoustic waves. The dependencies of the distribution of a mechanical displacement and electrical potential over the plate thickness for electrically open and electrically shorted plates have been plotted. The influence of a layer with arbitrary conductivity placed on a one or on the both plate surfaces on the profiles under study, phase and group velocities of the forward and backward acoustic waves in X-Y potassium niobate has been also investigated. The obtained results can be useful for development of the method for control of a particle or electrical charge movement inside the piezoelectric plates, as well a sensor for definition of the thin film conductivity.