A tutorial on the transfer matrix method for acoustic modeling

The transfer matrix method (TMM) is a common technique used to calculate the input impedance or reflectance for 1D acoustic systems that can be approximated in terms of concatenated cylindrical and/or conical sections, as well as side branches. Each section is represented by a transfer matrix that relates frequency-domain expressions of input to output in terms of pressure and volume velocity. This tutorial will provide a brief overview of the TMM formulation, followed by examples using an open-source implementation in Matlab. Methods to derive TMM characterizations for more arbitrarily shaped geometries and extensions for tonehole interactions will also be briefly discussed.