Coupling between Pressure and Temperature Waves in Liquid Helium

When the thermal expansion coefficient ($\alpha$) is retained in the linearized hydrodynamic equations of the two-fluid model of superfluid liquid helium, pressure and temperature waves are not independent. Thus a periodically varying temperature source produces not only temperature waves in liquid helium, but also two pressure waves $p_1^{\prime }$ and $p_2^{\prime }$, which propagate at the velocity of first and second sound, respectively. Similarly, a vibrating diaphragm produces not only pressure waves but also two temperature waves $T_1^{\prime }$ and $T_2^{\prime }$, which also propagate at the velocity of first and second sound, respectively. Lifshitz has shown that the amplitudes of these cross modes should be proportional to $\alpha$. An investigation of this coupling has been made by observing and studying the two pressure waves $p_1^{\prime }$ and $p_2^{\prime }$ produced by a heater and the temperature wave $T_2^{\prime }$ produced by a capacitor microphone. The temperature dependence of the amplitude of these waves has been studied using both pulse and standing-wave techniques in the temperature range from 1.2 K to the $\lambda$ point. Good agreement with theory has resulted only for the $p_1^{\prime }$ mode.