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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.
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