Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

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}


Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

[How to cite this work]  [Order a printed hardcopy]  [Comment on this page via email]

``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2023-08-20 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA