Sounds like the fuel pump is what is noisy. The fuel filter could be plugged, or the pump could be failing.
Low fluid level.
Where is the noise coming from? If its from the fenders or wheels is a much different problem than if its coming from the transaxle.
probably a wheel bearing
Check the bearings.
Check the wheel bearing.
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.
Most likely the power steering belt is old and should be replaced.
One or both of you're drive axle bearings is dry
I have a similar issue with my Stratus, except instead of humming, mine rumbles slightly. This answer is only speculation, but I believe that it happens because the power steering is stretched to the max while turned completely to the right. You'll hear a humming noise because the hydraulics are trying to pump even more fluid in order to turn further, but there isn't enough fluid in the system. Alternatively, your passenger-side front bearing could be worn out, but it would be much more noticeable than just a humming noise.
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
i had some type of problem with my Transmission it had a loud humming noise whenever i start, the humming would go away when ever i start moving, but when i came up to a stop sign or a red light the humming would start, my friend who is a very good repair in all type of automotive told me my transmission oil pump was bad, well after he change the transmission oil pump the problem was gone.