Calculation of the acoustical field of a semi-infinite cylindrical wave-guide by means of the green function expressed in cylindrical coordinates

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Authors

  • Anna SNAKOWSKA Institute of Physics, Higher Pedagogic School, Poland
  • Roman WYRZYKOWSKI Institute of Physics, Higher Pedagogic School, Poland

Abstract

The exact solution to the problem of the acoustic wave propagation is presented for a half-infinite cylindrical wave-guide with rigid walls, i.e., with taking into account the diffraction phenomena on the open end of wave-guide. The problem was solved by means of the theory of acoustic field without sources and the use is made of the Green's function method in the cylindrical space coordinates, leading to two integral equations which are solvable with the help of the Wiener-Hopf method. The wave number considered was taken to be a complex quantity, and the reduced forms of the final formulae are presented for the limiting case of real wave number.

References

[1] Lord RAYLEIGH, Theory of Sound, MacMillan, London 1940.

[2] W. RDZANEK, R. WYRZYKOWSKI, Acoustic field of a cylinder, WSP, Rzeszów 1975 (in Polish).

[3] H. LEVINE, J. SCHWINGER, On the Radiation of Sound from an Unflagged Circular Pipe, Phys. Rev., 73, 4, 383-406 (1948).

[4] L. A. WAJNSZTEJN, ZTF, 18, 10, 1543 (1948).

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