Why Does My Car Make A Humming Noise When I Accelerate?

If the sound that you are describing, is what I am hearing, the alternator is probably screaming.
When sitting in park, engine running, foot on brake, turn the steering wheel from side to side. If the noise increases, then it could be the power steering pump.
If the voltage regulator inside the alternator is bad, it would cause the alternator to work at full capacity, which would cause a noise.
Usually when noises like humming are described to me, it turns out to be a bad bearing in one of the belt driven components. 

I could be your alternator. It makes a humming noise when it is going bad.

Chevrolet 1996 1500 se mark 3 van is making a rear humming noise when I accelerate maybe 20 mph.

If this a front wheel drive vehicle and the steering wheel or the front end shakes during acceleration its usually a indication of a bad front axle shaft. By what you have described that's what it sounds like. If it would be the exhaust you can check this by doing a brake torque, this is done by starting the car put in drive, hold the brakes, and applying the gas until you get the hum or vibration.

My car is making a humming noise could it be gear box

Something may need to be aligned or the muffler needs to be looked at. Take to a mechanic right away.

It may be the muffler or a pump leak

Most likely your Wheel bearings are gone.

On that car you may have a Fan Clutch, that would mack that noise if there was a problem with the fan clutch.

Could very well be pre-ignition. If it sounds like sand dropped on a piece of tin this is the case and it's very damaging to your engine. You should get it checked out as soon as you can. This is normally caused by running gas which is too low of octane for your engine or timing that is too fast.

My car did that and it was a bad exhaust. I had to replace it because it eventually broke a bracket. When that happened it made a horrible vibration sound in first to second gear. Maybe they can look at it and just see if it is loose.

I have a 01 chevy venture and I have a humming noise in my engine and the temperature gadge rises up too.  I was told it was my water pump.  Is it possible.