I know I don't have an '11, but I heard it a few times from other members saying theirs does it too (past threads), mine does as well. So I've heard it for '08-10 years and I am pretty sure the entire power-train carried over for 2011.
pretty sure its just normal, just tranny whine. I have a jeep that does it too (or maybe from its transfer case...its in that general tranny area haha.)
z27ls3....

haha
edit: I'm like DavidHB below, 4th gear until like 47mph then drops into 5th gear at like 1400rpm