Abstract
The radiation of plane harmonic sound waves from a rigid stepped cylindrical waveguide is treated by using the mode-matching method in conjunction with theWiener-Hopf technique. The solution is exact, but formal, since infinite series of unknowns and some branch-cut integrals with unknown integrands are involved. Approximation procedures based on rigorous asymptotics are used and the approximate solution to the Wiener-Hopf equations is derived in terms of infinite series of unknowns, which are determined from infinite systems of linear algebraic equations. Numerical solutions of these systems are obtained for various values of the parameters of the problem and their effects on the directivity of the stepped waveguide is presented.
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References
H. Levine and J. Schwinger, On the sound radiation of sound from an unflanged circular pipe. J. Phys. Rev. 73 (1948) 383–406.
Y. Ando, On the sound radiation from semi-infinite circular pipe of certain wall thickness. Acustica 22 (1969/70) 219–225.
A. D. Rawlins, Radiation of sound from an unflanged rigid cylindrical duct with an acoustically absorbing internal surface. Proc. R. Soc. London A-361 (1978) 65–91.
A. Büyükaksoy and B. Polat, Diffraction of acoustic waves by semi-infinite cylindrical impedance pipe of certain wall thickness. J. Eng. Math. 33 (1998) 333–352.
A. H. Nayfeh and D.P. Telionis, Acoustic propagation in ducts with varying cross-sections. J. Acoust. Soc. Am. 54 (1973) 1654–1661.
S. W. Rienstra, Sound transmission in slowly varying circular and annular lined ducts with flow. J. Fluid. Mech 380 (1999) 279–296.
B. Nilsson and O. Brander, The propagation of sound in cylindrical ducts with mean flow and bulk reacting lining III. Step discontinuities. IMA J. Appl. Math 27 (1981) 105–131.
F. Birbir, A. Büyükaksoy and V. P. Chumachenko, Wiener-Hopf analysis of the two-dimensional box-like horn radiator. Int. J. Eng. Sci. 40 (2002) 51–66.
Y. Ando, Experimental studies of the pressure directivity and the acoustic center of the circular pipe horn loud speaker. Acustica 20 (1968) 366–369.
I.H. Sneddon, The Use of Integral Transforms. New York: Mc Graw Hill (1972).
A. D. Rawlins, A bifurcated circular waveguide problem. IMA J. Appl. Math. 54 (1995) 59–81.
S-W Lee, V. Jamnejad and R. Mittra, Near field of scattering by a hollow semi-infinite cylinder and its application to sensor booms. IEEE Trans Antennas and Propagat. AP-21 (1973) 182–188.
E. T. Whittaker and G. N. Watson, Modern Analysis. Cambridge: CLIP (1958) 608pp.
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Türetken, B., Büyükaksoy, A. & Demir, A. Radiation of sound waves from a rigid stepped cylindrical waveguide. Journal of Engineering Mathematics 46, 33–54 (2003). https://doi.org/10.1023/A:1022814918308
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DOI: https://doi.org/10.1023/A:1022814918308