Numerical modeling of axisymmetric sources in infinite baffle

Abstract

According to standards, characteristics of loudspeakers should be measured in an anechoic room with the use of sufficiently great rigid baffle. To achieve accordance of numerical calculations to results of measurements, the numerical algorithms for a source in an infinite baffle are needed. In the paper three boundary integral methods—the Huygens–Rayleigh (HR) integral method, the Kirchhoff–Helmholtz (KH) integral method, and the simple-source density (SSD) method—are explored for the sources of revolution with optional surface velocity distributions and shapes of cross sections (cone, flat piston, dome). It was shown that solution of the boundary-value problem for the KH and SSD methods exists and is unique for all frequencies. The HR method is numerically the simplest and is free of existence/uniqueness problems but is theoretically founded for a flat piston only, whereas for sources of other shapes it gives erroneous results. The problem of inclusion of an infinite baffle into the numerical model is easy to overcoming for the SSD method because an auxiliary source-density function rapidly decreases out of source and only a small fragment of the baffle influences the final result. For the KH method that question is more difficult because pressure on the baffle surface does not decrease sufficiently fast. The improved KH method that overcomes this deficiency is described.