Abstract
The paper presents the exact formula for the impedance of the outlet of a semi-infinite cylindrical wave-guide derived by considering the propagation of an arbitrary Bessel mode towards the outlet and accounting for the generation of all permissible mode due to the diffraction at the open end. For this purpose, the formula of acoustic potential as well as the expressions for the reflection and transformation coefficient were used. The results of numerical calculations of the real and imaginary part and the moduli of impedance for the diffraction parameter ka in the range 0-20 were presented on graphs.References
[1] Rayleigh Lord, Theory of sound, Mc Millan Company, London 1940.
[2] H. Levine, and J. Schwinger, On the radiation of sound from an unflanged circular pipe, Phys. Rev., 73, 383 (1948).
[3] L. A. Wajnshtejn, The theory of diffraction and the factorization method (Generalized Wiener-Hopf technique), Golem 1969.
[4] A. Snakowska, and R. Wyrzykowski, Calculation of the acoustical field of a semi-infinite cylindrical wave-guide by means of the Green function expressed in cylindrical coordinates, Archives of Acoustics, 11 (1986).
[5] A. Snakowska, and R. Wyrzykowski, Wybrane zagadnienia teorii dyfrakcji, Wydawnictwo WSP Rzeszów 1984.
[6] B. Noble, Methods based on the Wiener-Hopf technique for the solution of partial differential equations, Pergamon Press, London-N. York, 1958.
[2] H. Levine, and J. Schwinger, On the radiation of sound from an unflanged circular pipe, Phys. Rev., 73, 383 (1948).
[3] L. A. Wajnshtejn, The theory of diffraction and the factorization method (Generalized Wiener-Hopf technique), Golem 1969.
[4] A. Snakowska, and R. Wyrzykowski, Calculation of the acoustical field of a semi-infinite cylindrical wave-guide by means of the Green function expressed in cylindrical coordinates, Archives of Acoustics, 11 (1986).
[5] A. Snakowska, and R. Wyrzykowski, Wybrane zagadnienia teorii dyfrakcji, Wydawnictwo WSP Rzeszów 1984.
[6] B. Noble, Methods based on the Wiener-Hopf technique for the solution of partial differential equations, Pergamon Press, London-N. York, 1958.
