Solving one-dimensional acoustic systems using the impedance translation theorem and equivalent circuits: A graduate level homework assignmenta)

The natural frequency resonances and sound radiation from one-dimensional acoustic systems are of great interest in the study of musical instruments, human vocal tract effects on speech, automotive exhaust pipes, duct systems for temperature control in buildings, and more. The impedance translation theorem is an approach that may be used to solve for the input impedance and therefore the resonance frequencies of one-dimensional systems. Equivalent circuits offer another approach to solving one-dimensional systems, though with equivalent circuits you can also solve for the response at any location in the system, including the radiated sound pressure. At Brigham Young University, there are two graduate level courses that teach these two techniques. One of the most challenging and memorable homework assignments from these courses is based on using one of these techniques to analyze a particular acoustic system and compare its response with the real thing. This paper discusses the basics of these two techniques and applies them to an analysis of phonemes produced by altering the human vocal tract. Details about the homework assignments are also given.