Measurement of the Diffraction Coefficient of a Trihedral Cone with Homogeneous Neumann Boundary Conditions

We consider the scalar problem of diffraction by a trihedral cone with homogeneous Neumann boundary conditions. Such a problem can be obtained for one of the Debye potentials if one considers diffraction of an electromagnetic wave by a perfectly conducting cone or for the acoustic potential in the case of acoustic wave diffraction by a rigid cone. We approached the problem experimentally in the acoustic setting. Our goal was to measure the diffraction coefficient (the amplitude of the spherical wave scattered by the tip of the cone). The used cone occupied one-eighth of the space (vertex of a cube). Measurement method was based on using Maximum Length Sequence (MLS) as the input signal. Besides, we used volume velocity adapter (a tube with two microphones) to cancel out the frequency response of the acoustic source itself and to keep only the diffraction-related part of the system response. Volume velocity data processing was based on Weistein's theory of radiation from an unflanged cylindrical waveguide. Compared to the naive approach of taking the volume velocity proportional to the particle velocity in the two plane waves propagating in the tube, such data processing improves considerably the quality of the phase response measurement. Although the amplitude of the scattered spherical wave was about 100 times smaller than the amplitude of the incident wave, the proposed method allowed us to reach signal-to-noise ratio sufficient to determine the diffraction coefficient with a relative error of about 10%. The measurement results were compared with theoretical values showing very good agreement.