On the Radiation of Sound from an Unflanged Circular Pipe
- 15 February 1948
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 73 (4), 383-406
- https://doi.org/10.1103/physrev.73.383
Abstract
A rigorous and explicit solution is obtained for the problem of sound radiation from an unflanged circular pipe, assuming axially symmetric excitation. The solution is valid throughout the wave-length range of dominant mode (plane wave) propagation in the pipe. The reflection coefficient for the velocity potential within the pipe and the power-gain function, embodying the characteristics of the radiation pattern, are evaluated numerically. The absorption cross section of the pipe for a plane wave incident from external space, and the gain function for this direction, are found to satisfy a reciprocity relation. In particular, the absorption cross section for normal incidence is just the area of the mouth. At low frequencies of vibration, the velocity potential within the pipe is the same as if the pipe were lengthened by a certain fraction of the radius and the open end behaved as a loop. The exact value of the end correction turns out to be 0.6133.Keywords
This publication has 8 references indexed in Scilit:
- On a Class of Singular Integral EquationsJournal of Mathematics and Physics, 1941
- XLIV. The end - correction of an unflanged pipeThe London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1937
- VI.On the electrical and acoustic conductivities of cylindrical tubes bounded by infinite flangesThe London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1936
- LX. (i.) The end-corrections of an open organ flue-pipe; and (ii.) The acoustical conductance of orificesThe London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1930
- Effect of Frequency on the end Correction of PipesPhysical Review B, 1928
- LIII. Experiments for determining the correction to be added to the length of a cylindrical resonant tube to find the true wave-length, and the velocity of sound in small tubesThe London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1879
- XXVII. Notes on the theory of soundThe London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1877
- LXI. Acoustical observationsThe London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1877