l have a 2006 Dodge Ram 1500.When accelerating, the truck makes a humming sound.Does not appear to be related to shifting gears or RPM

you need to tell us what engine option this one has on it so we can help you ,its hard to answer that one without knowing what engine size it has,good luck and happy new years,

Check out the air filter. make sure nothing is in there that should not be. a clog in the air filter can make whistling & humming sounds.

Also, check the axel's, make sure there is nothing rubbing, touching, or rapped up in it. things like wire. may be touching the rims, & making a very fast clanking/humming sound.

One other thing. if u have a bug guard on the hood. make sure it is tight to the hood. he bug shield on our 08 dodge ram came lose, & made a humming sound that got louder as we sped up.

Hop l could help. HAPPY NEW YEARS!!! message me if u need more information.

Maybe a faulty ground somewhere?

Balance your tires.