Influence of acoustic modes on resonance properties of a quartz tuning fork immersed in superfluid ⁴He and liquid mixtures ³He–⁴He

The oscillating quartz tuning fork method has been used to study resonance phenomena in experimental cells of different sizes filled with superfluid ⁴He and concentrated liquid mixtures of ³He–⁴He. An analysis of the temperature dependence of the resonance frequencies of the tuning forks showed that in a number of cases, the incompressible fluid model is not sufficient to interpret the experimental results and that acoustic processes in the cell should be taken into account. The frequencies of the resonances of the first sound in cylindrical geometry are estimated and their influence on the resonant frequencies of the tuning fork is shown, which can lead to a distortion of the shape of the resonant line. A comparison is made between experimental results for superfluid ⁴He and mixtures of ³He-⁴He with light isotope concentrations of 5% and 15%. It is shown that, in contrast to pure helium, the model of a viscous incompressible fluid cannot be applied to mixtures, even in the absence of first acoustic resonances. This can be explained by the fact that, when studying concentrated solutions, the excitation of the second sound along with the first can have a noticeable effect on the resonance characteristics of the tuning fork.