  In pure superfluid $^3$He-B at ultra-low temperatures, quartz tuning fork
oscillator response is expected to saturate when the dissipation caused by the
superfluid medium becomes substantially smaller than the internal dissipation
of the oscillator. However, even with small amount of $^4$He covering the
surfaces, we have observed saturation already at significantly higher
temperatures than anticipated, where we have other indicators to prove that the
$^3$He liquid is still cooling. We found that this anomalous behavior has a
rather strong pressure dependence, and it practically disappears above the
crystallization pressure of $^4$He. We also observed a maximum in the fork
resonance frequency at temperatures where the transition in quasiparticle flow
from the hydrodynamic to the ballistic regime is expected. We suggest that such
anomalous features derive from the superfluid $^4$He film on the oscillator
surface.
