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When a wave travels from one medium to another, it gets reflected at the boundary of the second medium. A common example of this is when a person yells at a distance from a cliff and hears the echo of their voice. The sound waves (longitudinal waves) traveling in the air are reflected from the bounding cliff. Similarly, flipping one end of a string whose other end is tied to a wall causes a pulse (transverse wave) to travel through the string, which gets reflected upon reaching the wall. In...
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Related Experiment Video

Updated: Mar 15, 2026

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing
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Maximum bow force revisited.

Robert Mores1

  • 1Hamburg University of Applied Sciences, Finkenau 35, 22081 Hamburg, Germany.

The Journal of the Acoustical Society of America
|September 3, 2016
PubMed
Summary

This study introduces a bowing pendulum for precise violin friction measurements, finding Schelleng's model with Schumacher's velocity term best fits cello bowing dynamics.

Area of Science:

  • Acoustics
  • Musical Instrument Physics
  • Friction Dynamics

Background:

  • Existing violin bowing models (Schelleng, Askenfelt, Schumacher) lack confirmed friction coefficients.
  • Measurements of Helmholtz and non-Helmholtz motion regimes lack precise friction data.

Purpose of the Study:

  • To construct a bowing pendulum for accurate measurement of bowing parameters, including friction coefficients.
  • To validate and refine existing violin bowing models using empirical data.

Main Methods:

  • A novel bowing pendulum was developed for precise parameter measurement.
  • Two cellos were tested across all strings with varying bow-bridge distances.
  • Friction coefficients and adaptive impedance bowing were analyzed.

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Main Results:

  • Schelleng's model combined with Schumacher's velocity term provided the best fit for cello bowing.
  • Empirical data confirmed the stability of Helmholtz and non-Helmholtz motion regimes.
  • Transitions between regimes demonstrated hysteresis, requiring parameter adaptation.

Conclusions:

  • The bowing pendulum enables accurate friction coefficient measurement, validating bowing models.
  • The study refines understanding of cello bowing mechanics and regime transitions.
  • Adaptive impedance mechanisms are crucial for stable bowing dynamics.