What can we learn about the wolf phenomenon from a linearized analysis?
Résumé
String players are well aware of a perverse phenomenon known as wolf notes. Physically, such undesirable effect results from severe interaction between string and body vibrations, which are coupled at the bridge, when the sounding note approaches the frequency of a low-damped body mode. The phenomenon invested considerable efforts to deal with string/body coupled system. Different approaches have been adopted to achieve nonlinear time-domain simulations, including methods based on wave propagation with reflections, as well as time-domain modal methods used by the present authors. Recently, our modelling approach for bowed bars was used to address the linearized modal dynamics of the bowed string/body coupled system. The stability analysis provides a range of instability for a pair of coupled modes as the playing frequency approaches that of the instrument body, suggesting that the basic mechanism of wolf phenomenon can be explained by a linearized approach. In this paper, we examine the features of the linearized modal dynamics of the bowed string/body coupled model and explore the influence of bowing parameters on the modal frequency and damping. The results from our linearized analysis show a dependence of the wolf beating frequency on the playing control parameters (bow normal force and tangential velocity), as observed in the nonlinear time-domain computations.
Domaines
Acoustique [physics.class-ph]
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