Nonlinear dynamics of the wolf tone production

Some bowed string instruments such as cello or viola are prone to a parasite phenomenon called the wolf tone that gives rise to an undesired warbling sound. It is now accepted that this phenomenon is mainly due to an interaction between a resonance of the body and the motion of the string. A simple model of bowed string instrument consisting of a linear string with a mass-spring boundary condition (modeling the body of the instrument) and excited by Coulomb friction is presented. The eigenproblem analysis shows the presence of a frequency veering phenomenon close to 1 : 1 resonance between the string and the body, giving rise to modal hybridation. Due to the piecewise nature of Coulomb friction, the periodic solutions are computed and continued using a mapping procedure. The analysis of classical as well as non-smooth bifurcations allows us to relate warbling oscillations to the loss of stability of periodic solutions. Finally, a link is made between the bifurcations of periodic solutions and the minimum bow force generally used to explain the appearance of the wolf tone. Superscript/Subscript Available

Automated summary

Some bowed string instruments, such as the cello or viola, are susceptible to a phenomenon called the wolf tone, caused by an interaction between resonance of the body and string motion, as well as Coulomb friction. Analysis of the eigenproblem and periodic solutions reveals the frequency veering phenomenon and the link between the bifurcations of periodic solutions and the appearance of the wolf tone.