Suppression of wolf-tone based on equivalent circuit model

Abstract

Large size bowed stringed instruments, such as cello can pose undesired phenomenon called “wolf-tone” when you play at the specific pitch. When it occurs, a body strongly vibrates and a bow leaps on a string continuously. So, we are trying to figure out the cause of the wolf-tone and control it effectively. Thus, we devised “body-string coupled model” where body and string are coupled at bridge, and “bowed-string model” which expresses the relation between frictional force and relative speed, as it is called “stick and slip motion.” We simulated using finite-difference time-domain method and figured out the result that reproduces particular string motion called “Helmholz motion.” In addition, we set two parameters, speed of bow and pressure of bow, and calculated sound wave, oscillation mode, and the number of stick and slip. Then, we got the result of some existence ranges for wolf-tone. On this simulation, we added a small resonator in order to suppress the specific resonance mode which provides wolf-tone and observed wave forms. Based on these simulation results, we verified its effect experimentally on a real instrument.