Ultrasonic Radiation from Constrained Piston Sources and Rings

Abstract

Quantitative knowledge of the ultrasonic field near a circular piezoelectric source radiating into a fluid is desirable for some uses (interferometry, absorption, and diffraction measurements). The exact theoretical solutions available for numerical calculations assume an ideal piston source, which is not necessarily correct in practice. Two studies of a non-ideal piston source are reported here: (1) If the piston is assumed to be partially constrained in its outer portions, the axial sound field can still be computed by the Rayleigh method. It does not differ markedly from the ideal case, in the region of greatest practical interest. Certain experiments which have been quoted as substantiating the ideal piston may therefore not be significant. (2) A circular ring source can be treated by King's method, in integrals of Bessel functions. Some non-ideal pistons are equivalent to assemblies of such rings. The narrow ring source has interesting properties: at moderate and large distances it produces a beam more highly directive than that from the circular source. The ring source also produces an axial intensity following the inverse square law, at short ranges, more closely than that of the circular source