Do you have Preston Garvey as your companion? I had to drop him because his freakin' laser rifle kept making annoying sparking sounds all the time - even when the weapon was holstered or I equipped him with a different one. That's the only thing that comes to mind. If that's not it, you may want to check out some audio driver updates. Or maybe you installed a mod?
You're probably a synth. Bang your forehead on some concrete a few times. That should fix it.
pkleiss makes a good point. The laser musket does make a humming noise.
No, I'm with Piper and she is not using an energy weapon.
Also, I've tried to drop all my weapons in a crate and leave, noise still there.
I'm not using any mods, I changed FOV and mouse acceleration in the .ini file, that's it
Is your mic on? Otherwise it sounds like interference with your keyboard. Try using a different USB slot. If you have a powered USB hub plug your headphones into that.
If lowering one of the sound sliders lowers the noise, it probably isn't a hardware issue. Instead, it sounds like a ini configuration issue or maybe some item you are carrying. You can test the latter easily enough, just drop all your gear in a container and walk away naked. If the sound persists, it isn't item related. That leave ini settings (IMO). If you rename your ini files to something else, I believe the game will recreate them from scratch, with default values. But I'm not 100% sure of this. If not, just rename them back to their originals.
And in case that's not it...
What graphics adapter and driver are you using? Is it up to date? Modern graphics cards also have an audio output over HDMI connections.
Have you tried installing the Steam Beta patch yet? I hear there is an update in there regarding sound issues, though not specifically yours.
I've tried running naked, still have noise. Restored the .ini files to default, didn't fix it either.
I'm running GTX 960 with driver version 359.00
Okay, lets try something drastic, if you haven't already.
Disable your steam cloud sync: Steam >> Settings >> Cloud
Untick the sync box, exit steam.
Then delete (or just move) all you old saves and ini files out of your user folder.
Start the game up as a first time player in happy-go-lucky Sanctuary.
Do you still get the noise now?