If you have a 2007-2009 XK series car, you may want to see if there is a TSB about differential whine. There is one for the S-Type and it turns out the XK and S-Types use the same differential. I just had a differential replaced in my 2005 S-Type. At about the same time my car was in for service a 2007 XK was in also for a new differential.

Mike