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Scattering at Impedance Changes

When a traveling wave encounters a change in wave impedance, scattering occurs, i.e., a traveling wave impinging on an impedance discontinuity will partially reflect and partially transmit at the junction in such a way that energy is conserved. This is a classical topic in transmission line theory [297], and it is well covered for acoustic tubes in a variety of references [299,366]. However, for completeness, we derive the basic scattering relations below for plane waves in air, and for longitudinal stress waves in rods.



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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-06-11 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA