If you mean a residential fuse box, then there is a few possibilities:
1: A loose connection in the circuitry is drawing a current near the limit af the fuse.
2: A apparatus is drawing a current near the limit of the fuse.
3: The breaker itself is worn - replace soon.
bad relay fuse
The fuse box has relays mounted in it. The clicking noise is most likely a relay that has gotten loud.
the humming noise is coming from a bad ground on you stereo
Certain types of tires may cause a brief humming noise after your initial acceleration. The transmission may also cause a brief humming noise.
I have heard that if you have papers or napkins in the glove compartment box they can get sucked into the air vent which then makes a humming noise that you can hear while driving and as you increase the speed the pitch of the noise gets louder.
Should be in or near the fuse box
this type of noise is usually created by one of the relays, within the fuse box. Open the box, locate the bank of relays(little square box's(larger than a fuse)) and when it is making a "clicking" noise, gently rest finger on each one and you will feel the vibration. Simply look at fuse box diagram to discover what that relay is for, and go from there. The sound is power being switched on or off to whatever that relay controls
is the humming coming from the front end of the vehicle? i have a 1996 explorer with the same issue. yes the noise come from the front but not all the time seems to make the humming noise when it gets hot
If a car has a loud humming noise when accelerating, it could be that the air filter is missing. The air filter housing might also be loose. A loud humming noise can also be a signal that there is something wrong with the alternator belt or the fan belt.
where is the humming noise coming from? if it's coming thru the speakers and matches the rev tone of the engine, then you have a bad ground in your stereo.
Not knowing what this fuse box is for is hard to say. For a house, any buzzing noise is not good, this indicates a leakage of electricity which is never good. There could be a weak fuse or loose wire and this can be dangerous. Have someone look at the fusebox to be on the safe side.
wheel bearing