Quartz Tuning Fork Pressure Gauge for High-Pressure Liquid Helium

We have measured the quality factor Q and the frequency f of a 32-kHz quartz tuning fork immersed in liquid 4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^4$$\end{document}He between 0.9 and 3.0 K, over pressures ranging from the saturated vapor pressure to ≈\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\approx $$\end{document}25 atm. At constant pressure, as a function of temperature, the quality factor and frequency have strong features related to the temperature dependence of the superfluid fraction. At constant temperature, Q depends on the superfluid fraction, while the frequency is a smooth function of pressure. The behavior is explained using a simple hydrodynamic model. The liquid helium viscosity is obtained from measured values of Q, and together with tabulated values of the helium density as a function of pressure and temperature, the frequency shift can be parameterized as a function of temperature and pressure. The observed sensitivity is ≈\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\approx $$\end{document}7.8 Hz/atm. The quartz tuning fork provides a compact low power method of measuring the pressure in the bulk liquid.