Theory of the double-tuned side-inlet side-outlet muffler

Abstract

The transmission loss (TL) curve of a simple expansion chamber (SEC) is characterized by periodic domes. Theory of double tuning of the extended-inlet extended-outlet chamber consists in dimensioning the extended inlet (EI) and extended outlet (EO) at half and quarter chamber length (minus the end corrections) so that three-fourths of the troughs of the SEC-TL curve are tuned out, by the quarter-wave resonances of the EI and EO. However, this does not explain the shape and overall lifting of the resulting TL curve. In the present article, an analytical expression has been derived for TL of the double-tuned side-inlet side-outlet (SISO) muffler. Comparison of this expression with that of the SEC muffler explains the entire shape of the TL curve and reveals two interesting and useful implications of double tuning. Barring sharp peaks at Helmholtz numbers of p, 2p and 3p, the base TL curve of the double-tuned chamber (DTC) is similar to that of the corresponding SEC, with effective chamber length reduced to one-fourth and the area expansion ratio increased to fourfold. Consequently, one dome of the DTC-TL spans over four domes of the SEC-TL, and the new wider dome stands 12 dB higher than the domes of the corresponding SEC-TL curve. The 1-D predictions have been validated against the 3-D FEM simulations. Exact matching of the locations of the first three sharp peaks of the TL curves indicates that no end corrections would apply to the quarter-wave resonators of the SISO muffler configuration.