Abstract
We investigate the damping experienced by quartz tuning fork resonators in normal and superfluid $^{3}\mathrm{He}$ as a function of their resonance frequency from 22 to 250 kHz and contrast it with the behavior of the forks in $^{4}\mathrm{He}$. For our set of tuning forks the low frequency damping in both fluids is well described by the existing hydrodynamic models. We find that the acoustic emission becomes the dominating dissipation mechanism at resonator frequencies exceeding approximately 100 kHz. Our results show that the acoustic emission model used in $^{4}\mathrm{He}$ fluid also describes acoustic damping in superfluid $^{3}\mathrm{He}$ and normal $^{3}\mathrm{He}$ at low temperatures using the same geometrical prefactor. The high temperature acoustic damping in normal $^{3}\mathrm{He}$ does not exceed prediction of this model and thus the acoustic damping of moderate frequency devices measured in $^{4}\mathrm{He}$ should be similar or smaller in $^{3}\mathrm{He}$ liquid.
Highlights
The interaction of helium fluids with small mechanical resonators has traditionally being studied using vibrating wires, and has led to observations of the quantization of vortices in superfluid 4He [1,2], nucleation of quantum turbulence [3,4], and Landau critical velocity in superfluid 3He [5]
It is known that cavities suppress acoustic emission [18,56] and while the camera has an open cylinder geometry its effect on the fork’s acoustic emission is determined by their relative positions and orientation
The 4He data in the top panel contrasts the bulk measurements [22] shown in Fig. 2 using faded colors against the measurements in the cylindrical cavity for superfluid and normal 4He in bold colors
Summary
The interaction of helium fluids with small mechanical resonators has traditionally being studied using vibrating wires, and has led to observations of the quantization of vortices in superfluid 4He [1,2], nucleation of quantum turbulence [3,4], and Landau critical velocity in superfluid 3He [5]. Since the 2000s quartz tuning forks have become an established tool to investigate quantum solids [6] and liquids [7–10], where they have been used in studies of the viscosity [7], solubility of 4He-3He mixtures [10], Andreev retroreflection of quasiparticle excitations in superfluid 3He [16], and in turbulence studies in both helium isotopes [17–21]. The main reasons for the forks’ popularity are their high intrinsic quality factor, commercial availability, compact size, and the ease of use Their working procedures are well documented [8,11,33] and after calibration they can be used as temperature probes [8,12] or pressure gauges [14,15].
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