On the nonlinearity of a tuning fork

TL;DR

This paper presents an accessible experiment for measuring the nonlinear resonance behavior of tuning forks, demonstrating phenomena like softening curves and jump phenomena with high accuracy, suitable for educational and research purposes.

Contribution

It introduces a cost-effective, easy-to-operate experimental setup using Doppler interferometry to observe nonlinear tuning fork behaviors, expanding educational and research tools.

Findings

Observation of nonlinear behaviors such as softening tuning curves

Detection of jump phenomena in tuning forks

Measurement accuracy within ten microns

Abstract

Tuning fork experiments at the undergraduate level usually only demonstrate a tuning fork's linear resonance. In this paper, we introduce an experiment that can be used to measure the nonlinear tuning curve of a regular tuning fork. Using double-grating Doppler interferometry, we achieve measurement accuracy within ten microns. With this experiment setup, we observe typical nonlinear behaviors of the tuning fork such as the softening tuning curve and jump phenomena. Our experiment is inexpensive and easy to operate. It provides an integrated experiment for intermediate-level students and a basis for senior research projects.