Approximate methods for the solution of the equation of acoustic wave propagation in horns

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Authors

  • Tomasz ZAMORSKI Institute of Physics, Higher Pedagogical School, Poland
  • Roman WYRZYKOWSKI Institute of Physics, Higher Pedagogical School, Poland

Abstract

In practice, there are acoustic horns designed for which the equation of wave propagation has no exact solution of compact form. The need, therefore, arises for approximate solutions, to be used. Accordingly, this investigation sought optimum methods for an approximate solution of the wave equation of a horn. It was assumed that the optimum method should combine the requirement of relatively little time-consuming calculation and the possibility of physical interpretation of the approximate formulae obtained. It was found that the WKB approximation which is recommended in the literature and has been taken directly from quantum mechanics, in general does not satisfy these requirements, and in addition it cannot be used at all in some cases. Therefore, another two approximate methods were developed and their properties analyzed.

References

[1] A. H. BENADE, E. V. JANSSON, One plane and spherical waves in horns with nonuniform flare, Acustica, 31, 2, 79-98 (1974).

[2] I. N. BRONSZTEJN, K. A. SIEMIENDIAJEW, A guide-book to mathematics for technologists and engineers, The Macmillan Company, New York 1963.

[3] J. E. FREEHAFER, The acoustical impedance of an infinite hyperbolic horn, JASA, 11, 467-476 (1940).

[4] E. JAHNKE, F. EMDE, F. LOSCH, Tables of higher functions, McGraw- Hill Book Comp., New York 1960, pp. 55-60.