Acoustic refraction and attenuation in cylindrical and annular ducts

Abstract

Previous work has shown that refractive effects in sound propagation can be calculated correctly only by treating the complete boundary value problem. Starting from a given acoustic source pressure distribution the field is to be calculated everywhere. Such a calculation is effected here for cylindrical and annular ducts. The eigenvalue problem resulting from the assumption of complete separability in all the variables is solved numerically for the lowest and the next ten additional eigenvalues β_φ and the corresponding eigen-functions φ_φ. These eigenfunctions are then combined by a least total error squared method to represent the initial pressure distribution. This procedure leads to the pressure pattern everywhere in the duct. The calculation of distinct eigenvalues is not entirely straightforward. Some guidance is therefore given as to how the eigenvalues may be located. Among a number of typical calculations, cases with wall admittance are presented. They show clearly that the combined refractive-attenuation effects are indeed complicated. Lowest mode calculations may be very misleading.