THE SCATTERING AT A CORNER WITH ABSORBING FLANKS AND AN ABSORBING CYLINDER

Abstract

This paper continues and terminates the sequence of the preceding papers [1–4] about sound fields in wedge-shaped spaces, and especially resumes the topic of reference [4] which deals with the scattering of sound at building corners and an absorbing cylinder which surrounds the corner. The corner flanks in [4] were supposed to be rigid, so the sound field could be synthesized with ideal wedge modes. The present paper continues the task of reference [4], but now the corner flanks are absorbing. A model of the arrangement is applied which uses a special case of the modal analysis in reference [1]. The field space is subdivided into ring-shaped zones with radiiri, and the wall admittanceGiof the absorbing flank in each zone is supposed to be inversely proportional to the radius,Gi(r)∽1/r, so that the average value of the model admittance in a zone 〈Gi(r)〉 equals the admittanceGof the flank. An admittance functionGi(r)∽1/r, is associated with wedge modes of a simple form. The model with the “stepping admittance flanks” is an approximate to the corner with the constant admittance if the number of ring-shaped zones is high enough, so that the variation ofGi(r) in the zones remains restricted. The absorbing cylinder around the corner is used here for two reasons: first, the stepping admittance model is singular at the corner, which is excluded by the cylinder to improve the corner shielding which was demonstrated in reference [4] for rigid corner flanks.