Propagation of second sound near T sub. lambda

Superfluid hydrodynamics for second sound, expanded to first order in {del}{rho}{sub {ital s}} and including second-sound damping and finite-amplitude effects, are cast into a boundary-value-problem format, suitable for calculating the resonant frequency in a second-sound cavity operating near the {lambda} point. This model is applied to the data of Marek, Lipa, and Philips, which showed deviations from a simpler model in the region close to the transition. We find that our model by itself cannot explain the deviations, but if a shift in the estimated location of {ital T}{sub {lambda}} is included, a significant improvement can be obtained. The critical exponent {zeta}, describing the divergence of {rho}{sub {ital s}}, was found to be {zeta}=0.6708{plus minus}0.0004, in good agreement with the renormalization-group prediction 0.672{plus minus}0.002. The range for the reduced temperature parameter was extended to {var epsilon}=2{times}10{sup {minus}7}, substantially closer to the transition than in the previous analysis of this data. The shift in {ital T}{sub {lambda}} can be considered acceptable if the data very near {ital T}{sub {lambda}} are reinterpreted. The effect of the {del}{rho}{sub {ital s}} term is shown to be important for {var epsilon}{lt}10{sup {minus}6}.