Certain types of tires may cause a brief humming noise after your initial acceleration. The transmission may also cause a brief humming noise.
possibly on of the belt pulleys or a vaccum leak
sounds like a motor mount is broken or a transmition mount. have those checked.
a humming noise is usually related to the fuel pump about to go. or u just have a really loud fuel pump and everything is fine.
A whistling noise indicates a vacuum leak.
A whining noise from the fuel pump indicates that your fuel pump is close to failing. You should replace your fuel pump to avoid being stranded or unable to start your vehicle. All fuel pumps will emit a humming noise, but if you can hear it from inside the car, replace your fuel pump in time.
the humming noise is coming from a bad ground on you stereo
It is probably the cover for your catalytic converter.
Replace the Harmonic balancer
Some times the impeller blades get bent into the housing causing noise
Sounds like you have an older 4 cylinder car. I had a Pontiac 2000 4 cylinder that did that.
assorted loose things