A Two-Resonance Guitar Bridge

Now let's consider a two-resonance guitar bridge, as shown in Fig. 9.6.

Like all mechanical systems that don't ``slide away'' in response to a constant applied input force, the bridge must ``look like a spring'' at zero frequency. Similarly, it is typical for systems to ``look like a mass'' at very high frequencies, because the driving-point typically has mass (unless the driver is spring-coupled by what seems to be massless spring). This implies the driving point admittance should have a zero at dc and a pole at infinity. If we neglect losses, as frequency increases up from zero, the first thing we encounter in the admittance is a pole (a ``resonance'' frequency at which energy is readily accepted by the bridge from the strings). As we pass the admittance peak going up in frequency, the phase switches around from being near (``spring like'') to being closer to (``mass like''). (Recall the graphical method for calculating the phase response of a linear system [449].) Below the first resonance, we may say that the system is stiffness controlled (admittance phase ), while above the first resonance, we say it is mass controlled (admittance phase ). This qualitative description is typical of any lightly damped, linear, dynamic system. As we proceed up the axis, we'll next encounter a near-zero, or ``anti-resonance,'' above which the system again appears ``stiffness controlled,'' or spring-like, and so on in alternation to infinity. The strict alternation of poles and zeros near the axis is required by the positive real property of all passive admittances (§C.11.2).

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.