An ultrasonic rotary horn intended to be excited at a frequency of from about 18 to about 60 kHz, which horn is a shaped, solid metal object having a rotational axis and a radial surface terminated by a first end and a second end. The diameter of the horn can vary from about 4 cm to about 19 cm. The width of the horn at the radial surface is in the range of from about 0.6 cm to about 13 cm. The thickness of the horn at its rotational axis is from about 0.6 cm to about 15 cm and is independent of the width of the horn at the radial surface. The horn has a mass in the range of from about 0.06 kg to about 30 kg. The diameter, width, and thickness values are selected for a desired frequency so that the horn, upon being excited by ultrasonic energy at such frequency which is input at the rotational axis at, and substantially perpendicular to, one or both ends, is adapted to resonate in a manner such that: (1) the excited end moves substantially in phase with the movement of the source of excitation; (2) the opposing end, whether or not it is actively excited, moves substantially out of phase with the movement of the excited end; (3) said radial work-contacting surface also moves substantially out of phase with the movement of the excited end; and (4) said horn exhibits a single nodal point at its geometric center.