My 2008 Sante Fe has only one irritating problem. At around 1950 rpm I get what sounds like a right rear exhaust system heat shield vibrating. In gear or out, hot or cold, as the tach passes just below 2000 rpm it can be heard and then with more or less rpm it's gone. Trying to hold a steady ~1950 rpm to find this noise is no easy trick . Any ideas?
Thanks

 

I was hearing something rattling when I would go over bumps back there and it turned out to be the license plate frame. I tucked some foam underneath it. I haven't had any sounds like yours, though.

 

I have a Nissan with a similar issue, there is a vibration at a specific point in the rpm range. The only thing it has in common with my santa fe is the CVVT/continously variable valve timing.

My opinion on my Nissan is that it is at a point where the valves and engine speed are at just the point of inefficiency and the engine vibration is greater. In your case, since engines and exhaust are all connected, there may be a point in your exhaust that reacts more to that vibrational frequency.