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Limiting Cases

The force-wave reflectance of an infinite impedance (rigid wall or ``open circuit'') is

$\displaystyle \hat{\rho}(s) = \frac{R(s) - R_0}{R(s)+R_0} = \frac{\infty - R_0}{\infty +R_0} = 1
$

Similarly, the force-wave reflectance of a zero impedance (free termination, frictionless surface, or ``short circuit'') is

$\displaystyle \hat{\rho}(s) = \frac{0 - R_0}{0+R_0} = -1
$

For velocity waves, we obtain the opposite results: rigid terminations are inverting, and free terminations are non-inverting.


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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