1977 Questions for all other cars Rear end

I have a 77 Truimph spitfire that I have bought from a friend. 50,000 miles on it as of now. The car has not seen much use in the past 10 years. My question is, With the diffrenctail bolted to the frame and the car being so light and small, is it possible to hear the diffrential making a light noise at low RPM? I replaced the rear spring and the three univesal joints becouse they were sticking. Now that I have all running good. I hear the diffrential right behind me make a slight noise. It is not howling or grinding just sounds like gears going around on each other. Being from the old big car days I don't know if the rear end normally makes noise.
My Wife wants to take a few days and go away with it, but I am sheepish on having to walk.