Something is out of balance, maybe the water pump is on its way out.
Worn Ball Joint
if its a front wheel drive vehicle then it could be the axels
I would have your exaust pipe looked at, it might be loose, or might even be missing a bracket.
Could be a worn out shock or wheel bearings. Is it 4 wheel drive?
Is it accompanied by a shuddering or vibration? You could likely have bad brake rotors.
It may be your catalytic converter. Ours did the same thing with an automatic transmission. We sometimes thought it was the transmission, then we received a recall on the converter. Took it in to be replaced, and no more rattling.
The rapid back and forth of air or other matter is the sounds vibration (vibration is the anwser).
Check your muffler pipes.
Check pLugs and wires and the vibration my be from brake pads or warped rotors
It would be different pich
bad transfer case
If it's coming from the rear, I would check either your catalytic converter or your muffler. Either could have pieces loose in them that would cause a rattling sound when you either push or release the throttle.