I am having the exact same problem. My car was just picked up yesterday and has under 200 miles on it. The issue occurs between 1000 - 1200 RPM's and it doesnt matter which gear it is at during the time. I have an Automatic V6.
To replicate the issue it starts at around 43-46 MPH in 6th Gear....this is about the time the transmission is in 6th at the stated RPMs. If you let off of the gas it goes away....if you add more gas it goes away....when you maintain speed at this RPM is gets the vibration or hum. It almost sounds like the Tranny is in too high of a gear for that speed and should actually be in 5th.
I then tried to drop the car to a lower speed of 35-38MPH in 5th gear which would be the same 1000-1200 RPM range. The vibration and sound starts up at this speed and RPM as well.
To diagnose the problem I put the car into Sport mode and paddle shifted up or down depending on the speed to change the RPM's. The vibration and sound went away. I am no mechanic or claim to know anything about the inner workings of the vehicle....but by simple trial and error I can only assume that the reason this is happening is that the transmission is in a higher gear than it should be at that RPM.
What should I do about this problem? Can the dealer change the shift points? Is the transmission bad? Is this something I just need to deal with and get used to?