THE EFFECT OF THERMAL-EXPANSION ON NONLINEAR FIRST AND 2ND SOUND IN THE WHOLE TEMPERATURE REGION OF HE-II

We consider one-dimensional, weakly nonlinear first and second sound w aves in He II. The first correction to the shock speed is computed for each sound mode. The expressions obtained are exact with respect to t he coefficient of thermal expansion beta. It is shown that the commonl y made assumption of negligible beta can lead to significant error in the shock speeds for first sound away from the lambda-line. This contr asts with the calculation of the linear sound speeds and the shock spe ed for second sound where the beta=0 approximation yields accurate res ults. Near the lambda-line, the exact expressions for both modes are s een to contain fundamentally different singularities than those found in the commonly employed beta=0 theory. (C) 1996 American Institute of Physics.