A Terminating Resonator

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Index: Physical Audio Signal Processing

Physical Audio Signal Processing

Bridge Modeling

Passive String Terminations

Bridge Reflectance

The elementary impedance element in mechanics is the dashpot. — Click for http://ccrma.stanford.edu/~jos/pasp/Dashpot.html

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According to Hooke's law, the force F exerted by a spring stretched a distance x from its rest position is F=-kx. — Click for http://en.wikipedia.org/wiki/Spring_%28device%29

Click for http://hyperphysics.phy-astr.gsu.edu/hbase/mass.html#mas

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The wave impedance in a propagation medium relates the force-related component of the wave motion to the displacement-related component of the motion. — Click for http://ccrma.stanford.edu/~jos/OnePorts/Impedance.html

The wave impedance in a propagation medium is the force variable (such as pressure for acoustic waves) divided by the velocity variable. In ideal plane waves and traveling waves, the wave impedance is a real, positive number. For spherical waves in air, the wave impedance is different at each frequency. — Click for https://ccrma.stanford.edu/~jos/OnePorts/Impedance.html

Click for https://ccrma.stanford.edu/~jos/pasp/Ideal_Vibrating_String.html

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Index: Physical Audio Signal Processing

Physical Audio Signal Processing

Bridge Modeling

Passive String Terminations

Bridge Reflectance

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

, spring

, and dashpot $\mu$ (§7.2). More general bridge impedances can be modeled as a sum of such terms. Since the bridge is passive,

is positive real (§C.11.2).

**Figure 9.5:** Ideal vibrating string terminated by a second-order driving-point impedance consisting of a mass , spring , 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 © 2024-06-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

A Terminating Resonator

``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4 Copyright © 2024-06-28 by Julius O. Smith III Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2024-06-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University