A detailed tutorial for evaluating in-duct net acoustic power transmission in a circular duct with an attached cylindrical Helmholtz resonator using transfer matrix method

Abstract

The transfer matrix method has been extensively explored by many researchers for analysing acoustic duct systems. However, there does not exist a comprehensive source that elaborates the use of transfer matrix method for evaluating the performance of acoustic filters. The current approach describes a detailed step-by-step method for evaluating in-duct net acoustic power transmission for a harmonic plane wave travelling in a circular duct with an attached cylindrical Helmholtz resonator using the transfer matrix method. The net acoustic power transmission is evaluated using two different methods: (1) the product of acoustic pressure and acoustic volume velocity at the duct exit, and (2) estimates of the in-duct sound field using the two-microphone technique.