Measured Guitar-Bridge Admittance

Figure 9.7: Input admittance of a real classical guitar bridge measured by striking the bridge with a force hammer in the vertical direction.

A measured driving-point admittance [271] for a real guitar bridge is shown in Fig. 9.7. Note that at very low frequencies, the phase information does not appear to be bounded by $\pm\pi/2$ as it must be for the admittance to be positive real (passive). This indicates a poor signal-to-noise ratio in the measurements at very low frequencies. This can be verified by computing and plotting the coherence function between the bridge input and output signals using multiple physical measurements.^10.5

Figures 9.8 and 9.9 show overlays of the admittance magnitudes and phases, and also the input-output coherence, for three separate measurements. 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.

Figure 9.8: Overlay of three successively measured input admittances of a classical guitar bridge, displayed over a wider frequency range, and showing the coherence function, normalized to lie on the same dB scale as the admittance magnitude data.

Figure 9.9: Overlay of unwrapped phase data for three successively measured input admittances of a classical guitar bridge, displayed over the frequency interval for which the coherence is very close to 1 (also shown). There is an unknown phase offset due to measurement errors at low frequencies. Since the guitar bridge is passive, its admittance is positive real, so the phase must lie in the range $(-\pi /2,\pi /2)$ .