This started in the last week. First, we know we have one broke engine mount, but the noise just started so not sure if related or not. When we start the car, it has always idled a little high for a minute, then drops down and all is well. Now, the initial "roar" is louder with a roughness to it. Next, when I shift into reverse, the car makes a very loud (loud inside the cabin, not so loud standing outside) grinding/rattle sound, appears to come from the passenger side of the engine compartment. It will also do this when coasting down a hill or anytime I'm not in the gas or on the brake. It is an automatic, so the car is in drive while coasting. After some time driving, the noise seems to totally fade away. Any ideas or similar experiences?

 

Fix the motor mount