i have this issue, but its more a drone than a whine, increased noticeably above 40mph, ive had a few people check it out, the consensus is that the diff is badgered in some way.
Try the test they did for me, which was to get to motorway cruising speeds, preferably on a smooth road, then put the car into neutral and coast along, if the sound picks up considerably as did mine, then its the limited slip differential (according to the engineers)
I have just got myself a second hand diff and am waiting to fit it,
i'll let you know on the outcome,