Sensitivity Study of Source Impedance for Mufflers using the Moebius Transformation

Source impedance influences reflection from the source and is necessary to accurately predict the sound pressure level at a muffler termination. However, methods for measuring or simulation to obtain source impedance are expensive and computationally intensive. It has been observed that the equations relating source impedance to acoustic response are in the form of the Moebius transformation, which maps straight lines or circles in one complex domain into straight lines or circles in another. It can be proved that for variation of source impedance in a given range, the acoustic response range can be predicted quickly using the Moebius transformation. A sensitivity study on source impedance was performed on a muffler to demonstrate the approach.