Performance of Reactive Acoustic Mufflers

reactive muffler

expansion chamber

quarter-wave resonator

comparison

cross-section area ratio, m

14

cross-section area ratio, n

0.7

expansion chamber solution

quarter-wave tube solution

This Demonstration represents analytical, closed-form solutions for the transmission loss of two common reactive mufflers, an expansion chamber and a quarter-wave resonator. These closed-form solutions are assumed to be accurate only at low frequency where only plane waves are involved. The analytical models were derived using continuity conditions at each change of cross-sectional area [1]. The analytical models assume rigidity.

Muffler performance determined by transmission loss is governed by the cross-sectional area ratio of expansion chamber to pipe

m

, the cross-sectional area ratio of quarter-wave resonator to pipe

n

, wavenumber

k

, and muffler length

L

. As ratios

m

and

n

increase, the performance of each respective muffler improves. Resonances and anti-resonances are also clearly recognizable. A comparison plot is also presented in order to give the reader a generalized idea about muffler performance of a combined expansion chamber/quarter-wave resonator.