Toilet Takeoff

Our downstairs toilet has been making some odd noises lately, kind of like an airplane taking off. Listen to this video and see if you can figure out what's making the noise. It kicks in about forty seconds into the tank refill and stops when the tank is full. I've checked the house's plumbing but the only change was the removal of the outside faucet and the toilet sounded fine after that. It's really loud with the tank lid off but could that just be because it's the end of the pipe? Everything works fine, just noisy. I'd hate to replace a functional valve and find out it's not the problem. Any ideas?