Velocity and Attenuation of First Sound near theλPoint of Helium

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Abstract

The velocity and attenuation of first sound have been measured to within microdegrees of the $\ensuremath{\lambda}$ transition of liquid helium at a frequency of 22 kc/sec. Relative sound-velocity measurements of 1 part in ${10}^{5}$ could be obtained. The attenuation reaches a maximum about 1 or 2 \ensuremath{\mu}deg below the transition while the velocity minimum occurs 6 \ensuremath{\mu}deg below ${T}_{\ensuremath{\lambda}}$. Above the transition, the sound velocity satisfies the necessary condition for the validity of the Pippard-Buckingham-Fairbank relations out to at least 6 mdeg from the $\ensuremath{\lambda}$ point. Below ${T}_{\ensuremath{\lambda}}$, the velocity shows an added temperature dependence beyond that expected from the Pippard-Buckingham-Fairbank relations, which is proportional to ${|{T}_{\ensuremath{\lambda}}\ensuremath{-}T|}^{0,9}$. If this temperature dependence persists, the velocity of sound above and below the transition approaches a common value of 217.3 m/sec at the $\ensuremath{\lambda}$ point. Except in the immediate neighborhood of ${T}_{\ensuremath{\lambda}}$, the attenuation below the transition is proportional to ${|{T}_{\ensuremath{\lambda}}\ensuremath{-}T|}^{\ensuremath{-}1}$. This result is in agreement with the prediction of the Landau-Khalatnikov theory. Except in the immediate neighborhood of ${T}_{\ensuremath{\lambda}}$, the attenuation above the transition is proportional to ${|{T}_{\ensuremath{\lambda}}\ensuremath{-}T|}^{\frac{\ensuremath{-}1}{2}}$. This temperature dependence is not understood theoretically at present. Velocity dispersion results above and below the $\ensuremath{\lambda}$ point are also presented.

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