No mine is in the same narrow rev range you're talking about. Not only 1st gear, but any gear as long as it's the same range. After about 2 minutes in the morning, once the engine warms up it disappears. I'm assuming it's because the engine warms up, but don't know for sure.
If I drive out of my estate at less than ~2000 revs (2nd gear) then it doesn't do it. I've had my oil filter changed a few times since I've had the car and it didn't help me. I'd really like to know what it is, because it doesn't sound healthy, and it's quite loud.