Friction on a Bowed Violin String Fayette Shaw May 8, 2002

Outline Objective Background Experimental Setup Observation Techniques Conclusions

Objective To characterize the friction force at the bowing point with the following variables –Normal force –Bow velocity –Rosin layer thickness –Contact temperature Current models are not adequate

Traditional Models Linear model –Constant friction force characterized by coefficients µ k, µ s –F f = µ k F n Velocity dependent model –Functional dependence on bow velocity –Single value

Shortcomings Friction on a bowed string is not directly measurable Frictional force is cyclical The rosin is a dynamic system –Properties are time and temperature dependent Softening Viscosity Force is not single-valued for given velocity Physical system is history dependent

Helmholtz Motion Describes ideal string with rigid terminations and no energy losses –Bow movement supplies lost energy Slip-stick cycle String acts on rosin –Wear tracks –Softening-hardening

SEM image of wear tracks stick  | |  |  slip  |

Rosin What is rosin? –Intermediary between bow and string –Facilitates Helmholtz motion –Abietic acid and impurities –ClearTone™ Polymer which has properties which mimic rosin

Dynamic System

Laboratory Setup glass rod string nut bridge

Procedure Coat glass rod in rosin solution Make reference mark in rosin layer –Causes disturbance in data to correlate with images Run glass rod across E string (660 Hz)

Optical image of wear track and reference mark

Procedure Measure force at terminations of string From these measurements, the friction force can be reconstructed nutbridge

Observation Techniques CCD Camera –Used to obtain string deflection data Optical Microscopy –Ordinary microscope + camera Scanning Electron Microscopy (SEM) –CMU Materials Science Department

SEM close up image of stick

Conclusions Able to reconstruct friction force Able to calculate energy deposited during slip region of cycle Able to correlate forces to wear tracks

Conclusions Applications in –Tribology –Acoustics –Engineering Yeheudi Menhuin (1916–1999)

Image Credits

Thanks Undergraduate Research Initiative Prof. R.T. Schumacher and Prof. S. Garoff –Carnegie Mellon Physics Department