This just started on my car. As I lightly accelerate and get up to about 1800-2000 RPM's, there is a louder humming/vibration that occurrs. It goes away when accelerate harder. It also occurs in while the car is stopped and in park. I push the RPM's to almost 2K and you can hear it inside.

To me, it almost sounds like an exhaust leak, but, if it were that, I would guess it would make the sound all the time. I had my wife in the car holding the RPM's at 2k and I rolled around under the car and under the hood and nothing was apparent.

To try and pinpoint, it seems to be coming from the front passenger side area of the car. You can feel it in the floorboard.

A loose heat shield around the cat or other exhaust component could make that sort of noise.

There is a bracket that holds the fuel lines under the passenger side floor pan. Check to make sure the bolt didn't work itself loose or the bracket is not cracked/broken.

Not sure if you are still around,  but my 2011 SHO just started having the exact issue you have described. Did you ever get a diagnosis, and fix figured out.