If you have watched Thomas the Tank Engine (*) carefully you will have seen this effect mentioned. There is a certain amount of slack available in the U.K. style couplings on rail cars so that the engine can "pick up" one car at a time and get it moving before the coupling comes tight and the next car is picked up.
With U.S. style couplings I don't think that there's much slack, but as a train starts rolling you can definitely hear a kind of sequence of clanks as the couplings come tight from front to back.
(*) In the relevant episode a steam engine had broken its tie rods and had to work with less than the normal amount of traction. The remedy was to loosen up the couplings, providing more slack so that the relevant static friction would be on one car at a time.