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Related Concept Videos

Problem-Solving: Tuning of a Guitar String01:04

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In the case of stringed instruments like the guitar, the elastic property that determines the speed of the sound produced is its linear mass density or the mass per unit length. This is simply called the linear density. If the string's linear density is constant along the string, then the linear density is simply the total mass divided by the total length.
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The violin bow: taper, camber and flexibility.

Colin Gough1

  • 1School of Physics and Astronomy, University of Birmingham, B15 2TT, United Kingdom. profgough@googlemail.com

The Journal of the Acoustical Society of America
|January 10, 2012
PubMed
Summary

This study introduces a simplified violin bow model to analyze bending profiles and strength under tension. It reveals how bow hair tension significantly impacts flexibility and stability, preventing buckling.

Area of Science:

  • Physics of Musical Instruments
  • Mechanical Engineering
  • Acoustics

Background:

  • The behavior of a violin bow under tension is crucial for musical performance.
  • Existing models may not fully capture the complex interplay of forces and deformations.

Purpose of the Study:

  • To develop a simplified analytical model for the modern violin bow.
  • To describe bending profiles and strength as a function of bow hair tension.
  • To investigate the critical buckling loads and large deformation behavior.

Main Methods:

  • Introduction of an analytic, small-deflection model for a uniform cross-section stick.
  • Consideration of illustrative bending profiles (cambers).
  • Extension of analysis using non-linear, large deformation, finite element computations.

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  • Generalization of the Tourte bow taper model for various string instruments.
  • Main Results:

    • Demonstrated strong dependence of bow flexibility on longitudinal forces.
    • Showed forces comparable to critical buckling loads, risking excessive sideways buckling.
    • Extended analysis to tensions exceeding the critical buckling strength for straight sticks.

    Conclusions:

    • The simplified model accurately describes bow bending profiles and strength.
    • Bow hair tension is a critical factor influencing bow stability and performance.
    • The generalized taper model provides a framework for analyzing different string instrument bows.