I have a 1997 Ford Explorer that I am very happy with except for one thing. There is a noise which seems to be coming from the transmission intermittently. It's a weird humming/vibration sound that often happens on startup while the idle speed is changing. Then again it can also happen out of the blue when accelerating from a stop. I haven't brought it to the dealer yet, but my private mechanic looked it over and couldn't find anything. I'm really worried that it may be an expensive transmission problem that isn't going to get serious until my warranty is up.
The Ford Explorer has been having some low engine speed noise problems which often emanate from the transmission area, but not the transmission itself. Let's start with a simple and common cause first. As with many other makes and models, the tin heat shields which cover all or part of the exhaust system often come loose and cause various "buzzing and rattling" type noises. These sounds vary with engine RPM and load. In your case the shield on the catalytic converter is a good possibility as a cause, considering that it is positioned near the transmission. Ford puts out a "worm clamp" (Part # FOTZ-5A231-A). It's merely a big hose clamp that works really well at securing the heat shields and eliminating various noises.
The next possibility gets a little more complicated. The engineering of the Explorer's drivetrain has produced some noise problems due to vibrations being transmitted from the engine, through the exhaust and to the body by means of the exhaust-to-body mounting points. Ford Technical Service Bulletin: #97-7-6 has come out with a couple of modifications designed to deter the problem. First they want a new design muffler/tailpipe assembly installed with specific instructions in reference to the torque and positioning of the system. Next is the reprogramming of the PCM (Power Control Module). The reasoning behind the updated calibration is to alter the idle speed parameters and cut down on the time the engine spends at the high vibration points on the tachometer.
These are the two best places to start tracking down the condition that you've described.