Acoustic length correction of closed cylindrical side-branched tube

A numerical approach based on the three-dimensional boundary element method (BEM) is developed to determine the acoustic length correction of closed cylindrical side-branched tube mounted perpendicular to a cylindrical main pipe. The effects of Helmholtz number and finite length of side-branched tube on the acoustic length correction are examined, and a curve-fitting expression is provided for the acoustically long side-branched tube. For a pipe-mounted concentric Helmholtz resonator, the transmission loss and resonance frequency are predicted by using the 3-D BEM and the corrected 1-D analytical approach to assess the accuracy and applicability of the latter, as well as to illustrate the importance of acoustic length correction for an accurate prediction of resonance frequency of the pipe-mounted resonator.