  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.
