Geometric control of topological dynamics in a singing saw

TL;DR

This paper reveals how the localization of acoustic modes in a singing saw is governed by topological principles related to spatial curvature, enabling geometric control of its resonant properties.

Contribution

It uncovers a topological basis for localized modes in a singing saw, linking geometry and topological insulators to control acoustic localization.

Findings

Spatial curvature controls mode localization.

Experimental and theoretical validation of topological localization.

Potential for designing geometrically tunable high-quality resonators.

Abstract

The common handsaw can be converted into a bowed musical instrument capable of producing exquisitely sustained notes when its blade is appropriately bent. Acoustic modes localized at an inflection point are known to underlie the saw's sonorous quality, yet the origin of localization has remained mysterious. Here we uncover a topological basis for the existence of localized modes, that relies on and is protected by spatial curvature. By combining experimental demonstrations, theory and computation, we show how spatial variations in blade curvature control the localization of these trapped states, allowing the saw to function as a geometrically tunable high quality oscillator. Our work establishes an unexpected connection between the dynamics of thin shells and topological insulators, and offers a robust principle to design high quality resonators across scales, from macroscopic instruments to nanoscale devices, simply through geometry.