Acoustics of a flanged cylindrical pipe using singular basis functions

The problem of acoustic radiation from a cylindrical pipe with an infinite flange has been discussed in a number of papers. The most common approach i s to decompose the field inside the pipe over a basis of Bessel functions. A very large number of basis functions is usually required, with a large de gree of ripple appearing as an artifact in the solution. In this paper it i s shown that a close analysis of the velocity field near the corner yields a new family of functions, which are called "edge functions." Using this se t of functions as test functions and applying the moment method on the boun dary between the waveguide and free space, a solution is obtained with grea tly improved convergence properties and no ripple. (C) 2000 Acoustical Soci ety of America. [S0001-4966(00)02902-7].