Transverse and longitudinal forces of a string on the guitar bridge
Watson, Eric T.
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The force of a plucked string was measured at the bridge of a Kohno 30 guitar, and also at the end of a rack designed to simulate rigid end points. The string force was compared to the theoretical force function derived from the parallelogram model of a plucked string rigidly supported at its end points. Transverse as well as longitudinal amplitudes of force were considered for pluck displacements in the range 0 to 4 mm for a string 628 to 658 mm in length. Transverse force amplitude was in the range 0 to 3 newtons, while longitudinal force was about 7 to 10 times less. The Fourier coefficient magnitudes of the force function were measured and compared to coefficients of the rectangular waveform predicted from the parallelogram model. The relative phases between spectral force components determined for an actual plucked string were quite different from those of the rectangular waveform of force from the parallelogram model. These phase relationships among spectral components most drastically affected waveform appearance, as observed in reconstructed waveforms using calculated and measured phase relations. In longitudinal force measurements, proportionality of force F to pluck displacement d was measured. Exponent n applied to d was chosen to make force proportional to dn. Exponent n varied with tension, and was near 1.5 for typically-tuned nylon strings. This differs from parallelogram model which predicts that exponent n is independent of the static string tension, and that n - 2. Measurements also demonstrated that actual longitudinal waveforms were more complex than the model predicted.