An air-coupled ultrasonic transducer is created by bonding a bulk piezoelectric element onto the surface of a thick plate with a wedge of power-law profile. The wedge is used to improve the ultrasonic radiation efficiency. The power-law profile provides a smooth, impedance-matching transition for the mechanical energy to be transferred from the thick plate to the air, through the large-amplitude flexural waves observed in the thinnest region of the wedge. The performance of the proposed transducer is examined numerically and compared to that of a design where the piezoelectric element is isolated and where it is affixed to a thin plate of uniform thickness. The numerical analysis is first focused on the free-field radiation of the transducers. Then, time-reversal experiments are simulated by placing the transducers inside a cavity of arbitrary shape with some perfectly reflecting boundaries. In addition to time-reversal mirrors, the proposed concept could be integrated in the design of phased arrays and parametric arrays.