Lumped-Element Transmission-Line Analog of Sound in a Viscous Medium
Thomas L. Szabo · The Journal of the Acoustical Society of America · 1969
Interest in the transient of a wave in a viscous medium sparks the idea for a transmission-line analog of the viscous wave equation. For convenience, lumped elements are selected by the application of transmission-line-and-filter theory to simulate the transmission-line analog. Practical components for the model introduce additional parameters that cause the model to be better described by a higher-order, more general wave equation. Parameter choices are made to minimize the unwanted differences between the more realistic wave equation for the model and the viscous wave equation. The differential equation describing the actual model seems to have no easily attainable solution. However, a modified form of Blackstock's solution to the viscous wave equation is presented as a solution to a special case of the differential equation describing the actual model. Tone bursts injected into the completed model clearly show the presence of a precursor and a “postcursor.” Comparisons of the waveforms obtained experimentally and those predicted by the modified solution are shown and discussed.