SOUND RADIATED FROM A CYLINDRICAL DUCT WITH KELLERʹS GEOMETRICAL THEORY

An exact solution to the problem of radiation from a cylindrical duct has been available using the Wiener–Hopf technique for many years, and a number of approximate methods can also be considered. When parameter spaces involving high frequency are required, it is possible to use ray-theory-based techniques to solve the problem. Keller proposed such a method, introducing a geometrical theory of diffraction (GTD) which extended the concept of geometrical optics to account for diffracted rays. When a ray propagates inside the duct, it will reflect off the duct rim creating a Keller cone of singly diffracted rays, allowing formulae to be obtained for the singly diffracted field using Kellerʹs GTD. Expressions for the singly diffracted field are presented, and then compared with the exact solution for a range of parameters. The choice of parameters is governed by a set of mode angles which are used in describing geometrically how a ray propagates through the duct and out into free space.