• Accepted Paper

Unified theory of quartz tuning fork resonators

Hankyul Koh and Wonho Jhe

Phys. Rev. Lett. - Accepted 12 November, 2026

DOI: https://doi.org/10.1103/5jqp-ly73

Abstract

Quartz tuning forks, functioning as electrically driven piezoelectric resonators, have long served as exceptionally stable and widely adopted timing references in diverse domains of research and industry. Yet, experimentally measured electrical resonance spectra often exhibit resonance evolutions that remain unexplained within existing theoretical descriptions. Here we develop a unified continuum electromechanical modal framework that integrates piezoelectric electrodynamics, variational structural dynamics, and symmetry-selected electromechanical observability. Our theory quantitatively predicts the experimentally observed evolution of electrical resonance frequencies, demonstrating that electrical observability depends not only on the underlying mechanical eigenmodes but also on electrode-defined excitation and readout. The resulting framework unifies conventional coupled-oscillator, equivalent-circuit, and continuum descriptions within a single first-principles theory and provides a rigorous basis for precision electromechanical characterization.

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