A transmission matrix to generate four-pole parameters for a three-duct configuration is extended from the formulation for two-duct configuration. Theoretical and experimental results for zero-mean through flow type show the agreement in the low frequency region, but have some discrepancies in the high frequency region due to the two-dimensional effect.
By combining the various resonators into the three-duct concentric mufflers, a number of the transmission loss (TL) characteristics are found. It is observed that this type of muffler has a good sound attenuation characteristics in the high frequency region and especially large transmission losses are obtained when the porosities of the internal two pipes are high for the acoustically short case.
The expanded resonator has the merits of both the expansion chamber and the resonator for the acoustically short case and especially wide band and large attenuation is observed when the cavity of the acoustically short expanded resonator is packed with the absorptive material.
The Herschel-Quincke tube type three-duct muffler has a noticeable silencing performance improvement in the high frequency region than the conventional two-duct type muffler. And, if the absorptive material is packed in the three-duct type Quincke tube, it is found that the resonance frequency can be selected at will by controlling the density of the packing material and the transmission loss in the low frequency region is somewhat enhanced.
