Second sound resonances in superfluid 3He–4He mixtures

The resonances occurring during oscillations of quartz tuning forks in superfluid helium and its mixtures are studied. Quartz tuning forks are used to study various properties of helium, and also as a precision temperature sensor. Experimental observations of resonance phenomena were carried out in a wide range of temperatures and pressures, but the results of observations have not yet been exhaustively described theoretically. In this work we consider the pressure, entropy, and velocities oscillations in order to determine the conditions under which oscillations of a solid wall excite the first and second sound in superfluid helium and sound in supercritical helium, and to calculate the contributions of these processes to the formation of resonances during oscillations of closed tuning forks. In particular, the experimentally observed excitation of standing waves of pressure and entropy oscillations by an oscillating closed tuning fork, the appearance and properties of resonances depending on the temperature and pressure of helium are considered.