On the Radiation of Sound into a Circular Tube, with an Application to Resonators

The radiation from a plane piston into a rigid circular tube is treated. Consideration is given to the propagation of higher order sound waves. Curves of radiation impedance and pressure distribution are given together with an analysis of the elements of the equivalent impedance circuits. In addition to the closer study for special values of the tube's end impedance, some outline of the general case is given. Simplified measurements verify the calculations in the case of a tube closed by a rigid wall. Finally, the resonance frequency of cylindrical resonators is discussed.