This paper presents experimental results for the characteristics of acoustic waves propagating in a structure containing two parallel piezoelectric plates (I and II) separated by an air gap. Plate I, made of Y-X lithium niobate, contained two interdigital transducers that excited and received an acoustic wave with shear-horizontal polarization. Piezoelectric plate II, made of lithium niobate, was placed above and between the transducers, separated by a fixed gap. For its certain orientation, the amplitude-frequency characteristic showed sharply defined resonant attenuation peaks, which were situated at an equidistant separation from each other. The depth of the peaks was observed to decrease with a wider gap between the plates. It has been stated that these peaks are associated with the resonant reflections of a slot acoustic wave across the width of plate II. Experimentally determined phase velocities and electromechanical coupling coefficient for the slot wave in the structure under study are in a good agreement with theoretical values for various crystallographic orientations of plate II. A comparison between the experimental and theoretical results has allowed us to state two conditions for the slot wave to exist. The structures described may be employed for noncontact excitation of acoustic waves in the plates and for the development of various liquid, gas, and temperature sensors.