Okey dokey, let's give out a few numbers here:
Speed of sound is 340 m/s (assuming STP).
FFS tells us that we can design a weapon with a muzzle velocity of up to 6000 m/s, which is roughly Mach 17.5. It is noted that we can design our weapon to fire at 300 m/s, which is subsonic, and very nearly silent.
The weapon itself is going to make noise feeding ammo from the hopper into the barrel. Probably an electric motor whining. Imagine the minigun in Predator, after he'd expended all the ammo. Something like that for loudness.
Now, objects traveling at Mach 17.5.... Hmmm, I'm pretty sure that's not going to be quiet. Each round having several (hundred?) kilojoules behind it, you can be sure it will make a LOT of noise.
Unfortunately, I can't find anything quick and simple to tell me what that would be in dBa (audible decibels), but in electronic terms, that's 80 dBm (if delivered in 1 second, to make it watts instead of joules). If by some miracle that translates directly into dBa, then that's pretty loud.
So: the weapon itself will not make a lot of noise; not much more than most guns do nowadays (not counting the explosion of the powder). The round will make considerably more noise than modern guns, but there won't likely be a single loud bang. Perhaps imagine playing an explosion-sound on your computer, which crashes RIGHT in the middle of it and you hear the sound persistently... that might be what a VRF sounds like when firing it.
Hearing exactly where the round came from... I don't know. I DO know that I don't want to get in the way! Firing a stream of rounds is likely to get you found, though.