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