Measuring the Prong Velocity of Quartz Tuning Forks Used to Probe Quantum Fluids

Abstract

Recently, quartz tuning forks have been used to probe the dynamics of quantum fluids. For many of these measurements it is important to know the velocity amplitude of the tips of the vibrating fork prongs. We have used different techniques to establish, with an accuracy of a few percent, the relationship between the electrical and mechanical properties of several commercial quartz tuning forks with fundamental resonant frequency ∼32 kHz. The velocity is usually inferred from an electro-mechanical calibration that models a quartz prong as a clamped, rectangular cantilever beam. We have tested the accuracy of this calibration using three methods: measurement of the amplitude at which the fork prongs touch each other; direct optical measurement of the moving fork prongs using strobe microscopy; and a Michelson interferometry technique operating with a 670 nm laser. All three methods yield consistent results. The velocity so determined is found to be 10% lower than that of the standard electro-mechanical calibration.