RADIATION IMPEDANCE OF TUBES WITH DIFFERENT FLANGES: NUMERICAL AND EXPERIMENTAL INVESTIGATIONS

End corrections for open-ended cylindrical tubes are determined theoretically and experimentally. For the zero and low frequencies, the wave equation is solved numerically by using a finite difference method. For higher frequencies the complex radiation impedance is measured and for circular flanges, calculated with the boundary element method. For low frequencies the BEM links up with the FDM and for higher frequencies fits with experimental results. Various flanges found in particular in musical instruments are considered: circular flanges of various sizes, spherical and cylindrical flanges, square flanges, the normalised flange (used for loudspeaker testing), short flaring horns and a disk at a certain distance above the open end. Analytical fit formulas are proposed for each case.