This work is primarily comprised of five self-contained papers. Three papers are applications oriented. A common element in the first three papers is that micro-perforated panels (MPP), the permeable membranes in diesel particulate filters, and a source impedance are all modeled as a transfer impedance. The first paper deals with enhancing the performance of micro-perforated panels by partitioning the backing cavity. Several different backing schemes are considered which enhance the performance without increasing the total volume of the MPP and backing. In the second paper, a finite element modeling approach is used to model diesel particulate filters below and above the plane wave cutoff frequency. The filter itself is modeled using a symmetric finite element model and results are compared to plane wave theory. After the transfer matrix of the filters is known, it is used in three-dimensional finite and boundary element models. The third paper is a tutorial that shows how a source impedance can be modeled using transfer impedance approaches in finite element analysis. The approach used is useful for better understanding the resonance effects caused by pipes upstream and downstream of the exhaust. The fourth paper examines the best practice for the two-load transmission loss measurement. This method was integral to obtaining the measurements for validating the diesel particulate filter models. The fifth paper proposes transmission and insertion loss metrics for multi-inlet mufflers. It is shown that the transmission loss depends on the amplitude and phase relationship between sources (at the inlets) whereas insertion loss depends on both the source strength and impedance for each inlet.