From some old Summit Racing newsletters, I found the following: "Usually it is axle bearings, differential bearings, and pinion bearings that will generate a howling or whining noise. "
Depending on who's ears are listening, a howl and whine are the same.
Here's some more direction to get into the ballpark:
Noise: Howl while decelerating (gears previously quiet)
Cause: Loose pinion bearing preload
Noise: Howl with whir or rumble while accelerating at any speed (gears previously quiet)
Cause: Worn rear pinion bearing or worn gear set
Noise: Howl without whir or rumble while accelerating at any speed (gears previously quiet)
Cause: Worn gear set due to lack of lubrication or overloading
Noise: Howling while accelerating over a small speed range (gears previously quiet)
Cause: Worn gear set due to lack of lubrication or overloading
Noise: Howling after gear set installation
Cause: Faulty gears or improper installation
Noise: Low-pitch rumble at all speeds over 20 miles per hour
Cause: Worn carrier bearings
Noise: Whirring during acceleration/deceleration at about 10 miles per hour
Cause: Worn pinion bearings
Noise: Banging or clunking while making a turn, backing up, or rapid deceleration (like on a freeway off-ramp). Noise gets worse in warmer weather
Cause: Posi chatter due to improper lubrication; worn clutches or spider gears; improper assembly
Noise: Banging, crunching, or popping while making a turn. Noise not affected by temperature
Cause: Badly worn or broken spider gears
Noise: Banging or heavy clicking every two to three feet during acceleration and deceleration
Cause: Damaged or broken pinion gear tooth or teeth
Noise: Banging or heavy clicking every two to three feet during acceleration or deceleration, but not both
Cause: High spot or heavy chip on pinion gear tooth
Noise: Banging or heavy clicking every eight feet during acceleration and deceleration
Cause: Damaged or broken ring gear tooth or teeth
Noise: Banging or heavy clicking every eight feet during acceleration or deceleration, but not both
Cause: High spot or heavy chip on ring gear tooth
Noise: Clicking while decelerating from 20 miles per hour to a complete stop
Cause: Worn carrier case-side gear bores
Noise: Rumble or clicking that gets worse during hard turns
Cause: Bad wheel bearings
Noise: Driveline squeaking or grinding at any speed
Cause: Worn or damaged U-joints
Noise: Clunking when depressing the throttle pedal (takeoff)
Cause: Worn U-joints; worn spider gears; worn axle splines; excessive gear backlash; loose yoke splines; worn slip yoke splines
Noise: Clunk immediately after taking off from a stop
Cause: Worn slip yoke splines
Noise: Steady vibration that increases with speed
Cause: Worn U-joint or out-of-balance driveshaft
Noise: Cyclic vibration that varies in intensity. Intensity increases at a specific speed range, worsens during deceleration
Cause: Pinion angle too low (not parallel with front yoke on driveshaft)