One thing that anyone who will diagnose your problem via the internet will need is more information (the 3 M's) regarding your Cruiser; i.e. mileage, modifications, & maintenance.
Also, if you can be more specific about the problem itself. Is it a resonant humming sound? Does it come and go at a certain frequency? Or is it a constant sound that happens the entire time you are pressing on the gas pedal? Humming under acceleration is normally an indicator of U-Joints, and if they have gone bad, greasing them may not take care of the problem. On the other hand, I had a resonant hum at highway speeds that was caused by an out-of-balance tire.
The next time you hear it, put your hand on the transfer case lever (a pretty direct connection between the interior and the driveline) and see if you can feel a vibration that is in time with the noise.