## 5aMU14. Consideration of a device for correcting string vibration frequency measured by an electromagnetic transducer.

### Session: Friday Morning, December 6

### Time: 11:50

**Author: Atsushi Kuramoto**

**Location: Osaka Polytechnic College, 1778 Inaba-cho, Kishiwada-shi, Osaka, MA 596-01 Japan**

**Author: Masahiro Harazono**

**Location: Takamatsu Natl. College of Technol., Kagawa, MA 761 Japan**

**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.

ASA 132nd meeting - Hawaii, December 1996