The Mason horn, extension and applications

Abstract

Warren P. Mason, in the mid 1950s, introduced the inverted exponential horn as a concentrator of ultrasonic waves. In 1968, he published an extended account of a stepped approximation to the exponential horn. Part of the horn was replaced by a half‐wavelength piece that functioned as a mechanical transformer with a step reduction in diameter at the quarter‐wave point. The specimen was shaped like a dumbbell to give a mass‐spring‐mass resonance with a further step down in diameter. The result was a substantial reduction in area and thus an increase in vibratory stress. The apparatus may also be described as a composite resonant oscillator: Each of the three elements, transducer, transformer, and specimen, is at resonance. Mason developed the theory of this stepped horn only for perfect resonance, and allowed for damping only in the reduced part of the specimen. Here, his theory is extended to allow for small deviations from resonance, such as must occur in practice, and for damping in the other elements. When the damping and the deviations from resonance are small, simple sum rules hold. Variations in specimen design are also considered. Applications, past and future, will be discussed.