The Physical Interpretation of the Expression for an Outgoing Wave in Cylindrical Coordinates

Abstract

The sound field generated by a vibrating cylinder of infinite length, whose dynamic configuration is periodic in φ and z, is expressed in terms of acoustic impedance ratios. It is noted that symmetrical modes of vibration are suppressed at certain frequencies because the corresponding reactive impedance is infinite, and that all z-dependent modes become nonradiating below certain “cut-off” frequencies, the corresponding impedance being purely reactive. Graphs are presented for the impedance ratios corresponding to certain modes. For modes independent of z, the sound field is in the form of concentric cylindrical waves. For z-dependent modes, as the plane wave wavelength increases from zero to a certain critical “cut-off” value, the sound field successively assumes the form of a set of concentric cylindrical waves and of two sets of conical waves of decreasing vertex angle; at and beyond the “cut-off” point, the conical waves have degenerated into a set of plane standing waves normal to the z axis. Simultaneously the sound field has ceased being periodic in the radial direction, the phase velocity having become infinite. Practical applications of these phenomena are suggested.