Critical Ultrasonics Near the Superfluid Transition : Finite Size Effects

The suppression of order parameter fluctuations at the boundaries causes the ultrasonic attenuation near the superfluid transition to be lowered below the bulk value. We calculate explicitly the first deviation from the bulk value for temperatures above the lambda point. This deviation is significantly larger than for static quantities like the thermodynamic specific heat or other transport properties like the thermal conductivity. This makes ultrasonics a very effective probe for finite size effects.