Green's function derivations for specific acoustic admittances and impedances

Impedance and admittance relationships in acoustics are commonly given in their frequency-domain representations. This is done for many reasons including the simplicity of the mathematics used to compute frequency-domain impedance functions. However, although the frequency-domain representations of acoustical wave propagation typically have very neat closed-form solutions, there is a lack of intuition from the use of such techniques stemming from the added necessity of visualizing both a spatial and a frequency-domain dependence. Time-domain functions complement the frequency-domain constructs by providing new insight and intuition into important problems. The most common geometries under investigation for acoustics are those of a propagating plane wave, an outbound spherical wave, and an outbound cylindrical wave. For all three of these geometries, there exist fully developed frequency-domain techniques to derive the corresponding impedance and admittance functions. However since any frequency-domain function must have a time-domain counterpart, there should exist time-domain representations of these functions as well. Time-domain impedance and admittance functions for acoustical waves can be directly computed without the use of any frequency-domain methods or properties by using Green's functions. The strength of frequency- domain methods can also be realized since in simple geometries time-domain impedance functions can be easily calculated. However it is important to note that even in moderately complex geometries such as an outbound cylindrical wave, computing the time-domain impedance function can be difficult. The end goal of the time-domain analysis of acoustic impedance and admittance functions is an improved physical understanding of acoustic wave propagation. Although frequency-domain constructs are common, they do not provide this intuition. This thesis explores derivations of time-domain functions and provides improved intuition into these solutions