A handpiece having at least one set of piezoelectric elements polarized to produce longitudinal motion when excited at the relevant resonant frequency. The piezoelectric crystals are connected to an ultrasonic horn to which a cutting tip is attached. The horn and/or the cutting tip contains a plurality of diagonal slits or grooves. The slits or grooves produce optimized torsional movement in the cutting tip when the piezoelectric crystals are excited at a second resonant frequency.