A loud buzzing or whining noise when the transmission is in reverse may be caused by the regulator valve in the transmission valve body. A revised regulator valve was released that does not resonate. Careful diagnosis should be performed because other issues can create this same type of noise.Google+
Car Problem Reports
Dodge Dakota Regulator valve may cause noise when transmission is in reverse
Dodge Dakota Problem
Drive Train Affected: 2WD
Average Mileage: 67,500 mi (22,000 mi - 113,000 mi)
Visitor, 1996 Dodge Dakota, 2WD, 113,000 mi
I had noticed for a while this noise when backing up my truck. I have not yet attempted any repair.