Abstract:
An electromagnetic transducer is used for measuring characteristics of string vibration and for tuning stringed instruments. Analysis shows that, in spite of weakness of magnetic coupling between the transducer and the string, partial tones are not harmonic because of the influence of the negative stiffness of the transducer. Therefore, beats occur because of interference among the fundamental and the partial tones, whose amplitudes are not so small. This problem is formulated by use of linearized attraction to the static component and the stiffness component, and a (delta) function is used to express the lumped force in the distributed system. The solution can be obtained by use of a Laplace transform, and the vibration frequency affected by the negative stiffness is analyzed exactly from the numeric calculation of characteristic equation. This paper describes approximated equations for the vibration frequency based on these analyses and the measured frequency through the electromagnetic transducer. A method is described to correct the influence of negative stiffness on the vibration frequency using the measured frequency. The corrected results obtained from the prototype system show sufficient precision for practical use. Furthermore, according to the method, construction of a measurement device making use of the electromagnetic transducer is considered.