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 is 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 degree of ripple appearing as an artifact in the solution. In this paper it is 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 set of functions as test functions and applying the moment method on the boundary between the waveguide and free space, a solution is obtained with greatly improved convergence properties and no ripple.