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Complementary empirical data on minimum bow force.

Robert Mores1

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

The Journal of the Acoustical Society of America
|September 3, 2017
PubMed
Summary

The minimum bow force (Fmin) to sustain Helmholtz motion in stringed instruments depends on baseline force (Fmin,0), bridge resistance (R), and bow-bridge distance (β), challenging previous velocity-dependent models.

Area of Science:

  • Acoustics
  • Musical Instrument Physics
  • Vibrational Mechanics

Background:

  • Helmholtz motion (HM) is crucial for sustained sound on stringed instruments.
  • Previous models proposed Fmin proportional to bow velocity (vB), 1/R, and 1/β².
  • Recent studies suggested independence from vB and an overproportional effect of R.

Purpose of the Study:

  • To investigate the parameters governing the minimum bow force (Fmin) for Helmholtz motion.
  • To precisely control and measure parameters influencing string excitation.
  • To identify the transition regions between Helmholtz motion (HM) and non-Helmholtz motion (nHM-1).

Main Methods:

  • Utilized a bowing pendulum for precise control and measurement of bowing parameters.
  • Recorded string excitation at the contact point to classify motion types (HM, nHM-1).

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  • Focused measurements on transition zones between HM and nHM-1.

    • Main Results:

    • Empirical data from cello strings indicate a baseline force (Fmin,0) is required for HM, even at low bow velocities (vB).
    • This baseline force (Fmin,0) is dependent on bridge resistance (R) and relative bow-bridge distance (β).
    • Confirmed the 1/β² proportionality for HM maintenance.

    Conclusions:

    • The minimum bow force for Helmholtz motion is not solely dependent on bow velocity.
    • A fundamental baseline force, influenced by string impedance and geometry, is essential for initiating and sustaining Helmholtz motion.
    • Findings refine our understanding of the physics of bowed string instruments.