In the 1887 experiment by michelson and morley, the length of each interferometer arm was 11m. the experimental limit on the measurable fringe shift was 0.005 fringes. if sodium light was used (λ = 589nm), what upper limit did the null experiment place on the speed of the earth through the expected ether?

For the answer to the question above,
we can get the number of fringes by dividing (delta t) by the period of the light (Which is λ/c). 

fringe = (delta t) / (λ/c) 

We can find (delta t) with the equation: 

delta t = [v^2(L1+L2)]/c^3 

Derivation of this formula can be found in your physics text book. From here we find (delta t): 

600,000^2 x (11+11) / [(3x10^8)^3] = 2.93x10^-13 

2.93x10^-13/ (589x10^-9 / 3x10^8) = 149 fringes 

This answer is correct but may seem large. That is because of your point of reference with the ether which is usually at rest with respect to the sun, making v = 3km/s.