The Guitar Bridge

As a practical lumped-modeling example, consider the simulated admittance at a guitar bridge. A highly simplified simulated example is shown in Fig. M.2.

Like all lightly damped mechanical systems, the bridge must ``look like a spring'' at zero frequency and ``look like a mass'' at infinite frequency. This implies the driving point admittance must have a zero at DC and a pole at infinity; equivalently, the driving-point impedance must have a pole at DC and a zero 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''). Below the first resonance, we say the system is stiffness controlled, while above the first resonance, we say the system is mass controlled. This is a completely general characterization of any lightly damped, linear dynamic system. As we proceed up the axis, we'll next encounter a zero, or ``anti-resonance,'' above which the system again appears ``stiffness controlled,'' or spring-like, and so on in alternation to infinity.

A measured driving-point admittance [277] for a real guitar bridge is shown in Fig. M.3. Note that at very low frequencies, the phase information does not look like it should. This indicates a poor signal-to-noise ratio at very low frequencies. This can be verified by computing the coherence function for multiple measurements,^M.2 as shown in Figures M.4 and M.5. A coherence of 1 means that all the measurements are identical, while a coherence less than 1 indicates variation from measurement to measurement, implying a low signal-to-noise ratio. As can be seen in the figures, at frequencies for which the coherence is very close to 1, successive measurements are strongly in agreement, and the data are reliable. Where the coherence drops below 1, successive measurements disagree, and the measured admittance is not even positive real at very low frequencies.

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Subsections

• Building a Synthetic Guitar Bridge Admittance
  • Method 1
  • Method 2
  • Matlab for Method 1
  • Matlab for Method 2

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written by 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.