The dynamics of the musical saw

ORAL

Abstract

The musical saw is played by first being bent into an S–curve before it is bowed - this geometry allows for vibration modes that are localized near the point of inflection. To understand this, we consider how the spectrum of a curved plate or beam is controlled by a spatially varying curvature profile. Using a recent geometric interpretation of Anderson-like localization that links the underlying eigenvalue problem and a closely related elliptic problem allows us to determine the conditions for and extent of mode localization and suggests an explanation for the sweet sound of the saw.

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Presenters

  • Petur Bryde

    • Harvard University

Authors

  • Petur Bryde

    • Harvard University

  • L Mahadevan

    • Harvard University
    • SEAS, Harvard University
    • Paulson School of Engineering and Applied Sciences, Harvard University
    • Engineering and Applied Sciences, Harvard
    • John A. Paulson School Of Engineering And Applied Sciences, Harvard University
    • SEAS, Harvard
    • SEAS, Physics, OEB, Harvard University