Uncoupled multimodal wave reflection from guide termination with different flanges: Experimental and numerical investigation

Reflection of propagating modes is studied at the exit of a cylindrical acoustic wave guide from both an experimental and a numerical point of view. The plane mode and several purely azimuthal higher modes are extracted by means of modal decomposition and the uncoupled reflection coefficients of each mode are obtained using two microphonic antennas for Helmholtz numbers below 5.3. The reflection at the open end of the guide is studied for different guide terminations: without flange, with a finite flange, with an infinite rigid flange. A numerical model based on finite elements is set to mimic the experimental protocol: generation of the acoustic wave by a locally vibrating wall (to represent the flush-mounted loudspeakers used in the experiments), computation of the acoustic field in a cylindrical duct geometry and radiation in open space (represented by a half sphere). Results are also compared with the theoretical predictions from the literature when available. For the plane mode, the difference between the three sources of data is less than 5%; overall, the agreement allows to discern an effect of termination for the plane mode and for the first higher mode. An end with finite flange leads to intermediate behaviours between without flange and with an infinite flange only for the reflection coefficient of the plane mode.