Talk about the drone noise
 

I mentioned the other day I get a drone noise at 47-48 mph in my 2012 XKR convert. I hear it more with the top up as when it's down I have the Dynamic's on so the exhaust note drowns it out. The noise does not vary with speed and goes away at 50 mph and starts at 47 mph. I have 11,000 miles on the car with the original Dunlop 285/30-20's on it. Just curious if anyone else has this and if it is tire or drive train or brakes that is the cause. I'll bring it up next time I'm at the dealer.

I have a noise at those speeds but I think mine is related to the AC/Heat blower fan because when I turn it down just 1 click the noise stops

May be talking apples vs oranges here, as I have a 2007 XK, which gives me a slight 'howl' starting around the same speed, and the tone changes and gets louder when I let my foot up on the gas (gets quieter when accelerating).
I've been thinking it might be the differential, but not sure.

I get a drone/howl at 47-48 but it does not vary with speed. Not there under 47 and not there after 49. Interesting. Oh this is also the e-differential.

I wish I had some drone! The non performance exhaust is so quiet I can't hear a damn thing!

You're probably going too fast! ;-)

Let's be clear about something: the early XK cars (2007-08) had a droning noise (very irritating) at about 1200 rpm and above - right in the normal driving range. This was NOT a mechanical issue - it was resonance from the exhaust system - cured instantly by installing the Jaguar-designed fix: a bracket mounted between the exhaust and the transmission casing. My car had this noise when I purchased it; I had my dealer install the bracket (not cheap) and the noise disappeared instantly, never to return.

But the later cars should not have this same droning noise (although it is possible).

Do you recall if you could get that drone/resonance while not moving? i.e. foot on the brake and rev the engine up to 1200 (or above)?

Just curious, as my 'howl' only occurs while rolling, and since the sound changes, depending on whether I'm giving it gas, or not, I know its not a tire howl, and it seems to comes from the rear of the car, not below me.

I do not recall testing for this noise working the brake against the throttle (potentially harmful to the transmission), but given that your car is also an 07, the chances are that this is indeed the same droning noise I (and many others) had. If it comes on around 1200-1250 rpm, that's it.
In your query the statement "the sound changes, depending on whether I'm giving it gas or not" strongly suggests that this is an exhaust resonance issue. The bracket is an instant fix for this annoying noise. Trying to locate a noise in a car system is very difficult because noise travels...the noise in my car was also not "located" below me.

I took my car to an indy shop early this week to get an oil change, and have them do a general checkout of the car (first time I've had the car serviced since purchasing it last Nov). I told them about the howl (but didn't suggest where it might be coming from), and they confirmed that it was coming from the differential.
They suggested changing the diff fluid, as the least expensive first step.
I had them do that, and they reported the old fluid was very dirty, and had some 'shiny' stuff in it, possibly metal flakes. :(
I'm not sure if the fluid change affected the sound, as I haven't had a chance to drive it since getting it back.
They suggested changing the fluid again, in a month, to see if there any additional evidence of wear.

As for the 1200-1250 rpm drone, I have listened carefully, after reading your post, and yes I can say I also have that, but in addition to hearing it (much lower pitch than my differential howl), I can also feel it, a very soft vibration. Thanks for pointing it out, I'll investigate getting that bracket.

Could be a wheel bearing. I had a hum/Drone at 70mph and was convinced it was the diff. After a drive with the mechanic at Jag, he had seen and heard it before and they changed out the bad wheel bearing and all is good now. One of the way he diagnosed was turning the car and for that time ie. changing lanes, it could go away. Hope that helps