The acoustic impedance of liquid helium-3

Measurements have been made of the acoustic impedance (Z) of liquid $^3$He under its saturated vapour pressure in the temperature range 0.035 to 0.6 $^\circ$K. A 1000 Mc/s sound wave is propagated along the axis of an X-cut quartz crystal, and undergoes many reflexions from each end of the crystal. Values are obtained for the reflexion coefficient at an interface between quartz and liquid $^3$He by comparing the rate at which the signal decays in the crystal, with and without liquid $^3$He present on the ends. These values then lead directly to the acoustic impedance (Z) of the liquid. Usually, Z/$\rho$ (where $\rho$ is the density) should be equal to the velocity of sound, and above 0.1 $^\circ$K this is found to be so. However, at about 0.1 $^\circ$K the value of Z/$\rho$ increases abruptly, and at lower temperatures has a value about 10% greater. This result is in good agreement with Landau's theory of a Fermi liquid, which relates the change in impedance with the propagation of a new mode of sound, the so-called 'zero-sound'.