  We report the eigen-frequency shift induced by an applied voltage on quartz
material. The samples are in the form of commercial 32 KHz quartz tuning forks
used in watches. Three vibration modes are studied: one prong oscillates, two
prongs oscillate in the same and opposite directions. They all show a parabolic
dependence of the eigen-frequency shift on the bias voltage applied across the
fork, which is explained owing to the voltage-induced internal stress that
varies as the fork oscillates. Thus, this piezoelectric frequency effect is
possible to exist in all piezoelectric materials. The average coefficient of
the piezoelectric frequency effect is as low as several hundred nano-Hz per
millivolt, implying that the most precise (nano-Hz) yet fast-response
voltage-controlled oscillators and phase-locked loops can be built.
