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Ultrasonic dispersion relations in liquid helium Brown, Christopher Richard

Abstract

An experimental investigation of the velocity of sound in liquid helium at temperatures near 1° K was abandoned (at an early stage)^when the results of Whitney and Chase(16) became available. The original investigation, which had been motivated by the idea that the peak in the attenuation-temperature curve near 1° K is related to a corresponding feature in the velocity-temperature curve, evolved into a search for mathematical relations connecting the temperature variations of velocity and attenuation. Classical dispersion theory is reviewed, with emphasis on its physical and mathematical foundations. Applications of the theory in the fields of electrical network design, dielectric dispersion and ultrasonics are described in order to illustrate the use and the limitations of the Kramers-Kronig relations. The possibility of extending the scope of the Kramers-Kronig relations, by using variables other than frequency, is discussed. A brief sketch of the quantum mechanical basis of linear response theory is given in support of a proposal to use reciprocal temperature as a variable in dispersion-type relations. An attempt was made to apply dispersion relations in reciprocal temperature to the problem of ultrasonic propagation in liquid helium and a comparison of the predicted and the experimentally observed attenuations at the λ point was found to give encouraging results. The interferometer, to have been used in the proposed experiment is described.

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