The sound field generated by a vibrating cylinder of infinite length, whose dynamic configuration is periodic in φ andz, 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 allzdependent 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 ofz, the sound field is in the form of concentric cylindrical waves. Forzdependent modes, as the plane wave wavelength increases from zero to a certain critical cut‐off value, the sound field changes from a set of concentric cylindrical waves to 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 thezaxis. Simultaneously, the sound field has ceased being periodic in the radial direction, and the phase velocity in that direction has become infinite.Practical applications of these phenomena are suggested.