if you have a nvidia video card you can use msi afterburner to turn the fan speed up and see if the sound is your video card. there may be a few free fan control programs out there the let to change your cpu fan speed to see if it the fan. one thing i would do on any build is see where your wires are in your case. sometime when a fan spins up it can pull a wire into it. good power supply today have fan speed on them...they dont turn on till the temp in the ps hit a set point.
Definitely not the GPU fan (by the way it sounds like a hair-dryer at about 50% speed ).
I opened up Hardware Monitor and it shows and increase in the cpu fans RPM as I launch minecraft. I must thank you all.
It jumps from 615RPM to 915RPM when launching the game.
Is the game entirely CPU rendered? I do not experience this problem with any other games I play.