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A Terminating Resonator

Suppose a guitar bridge couples an ideal vibrating string to a single resonance, as depicted schematically in Fig.9.5. This is often an accurate model of an acoustic bridge impedance in a narrow frequency range, especially at low frequencies where the resonances are well separated. Then, as developed in Chapter 7, the driving-point impedance seen by the string at the bridge is

$\displaystyle R_b(s) \eqsp ms + \mu + {k/s}.
$

That is, the driving-point impedance is the series combination of a mass $ m$ , spring $ k$ , and dashpot $ \mu $7.2). More general bridge impedances can be modeled as a sum of such terms. Since the bridge is passive, $ R_b(s)$ is positive realC.11.2).

Figure 9.5: Ideal vibrating string terminated by a second-order driving-point impedance consisting of a mass $ m$ , spring $ k$ , and dashpot $ \mu $ .
\includegraphics[width=\twidth]{eps/f_yielding_term}


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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