A split-mode ultrasonic transducer is investigated in both theory and experiment. This transducer is a two-dimensional structure of periodically poled domains in a ferroelectric wafer with free surfaces. The acoustic vibrations are excited by a radio frequency electric current applied along the length of the wafer, which allows the basal-plane surfaces to be free of metal coatings and thus ready for further biomedical applications. A specific physical property of this transducer consists of the multiple acousto-electric resonances, which occur due to an acoustic mode split when the acoustic half-wavelength is equal to the domain length. Possible applications include ultrasonic generation and detection at the micro-scale, intravascular sonification and visualization, ultrasound therapy of localized small areas such as the eye, biomedical applications for cell cultures, and traditional nondestructive testing including bones and tissues. A potential use of a non-metallized wafer is a therapeutic application with double action that is both ultrasound itself and an electric field over the wafer. The experimental measurements and theoretical calculations are in good agreement.