There has been a very annoying noise since I bought the car in March of this year that sounds like a little like worn bearing that is most noticeable between 40 and 50 mph. It is for lack of a better description, wa wa wa wa sound that gets faster along with the speed and not so noticeable above 60 mph. and it seems to be coming from the rear. It is not a screaming loud noise and if the car was not so quiet otherwise, it could be missed altogether. When driving on rough concrete roads with a lot of tire noise, it can't be heard at all.
I have had the car in for service once at my trusty garage where they are not a Jaguar specialists but pretty knowledgeable overall and they tested for worn bearings in the rear and they even used a stethoscope but couldn't hear anything out of the ordinary. I don't think that drove it to hear the noise.

Does anyone have an idea what this might be? Anything peculiar to a 2005 S Type that others have experienced.

Any help will be appreciated.
2005 S Type 4.2
96,000 miles

Dennis