For us humans, this movements are slight and difficult to perceive most of the time. However, dogs are pretty keen on picking up “tail speak. Even if we don’t understand them, dogs totally do.
Also the speed of the wag its very important, for example: If the dogs sees someone known the dogs tail will move to the wright, but if they wag more slowly they are seeing someone unfamiliar to them.
Most tail speak is easy to decipher, if you know the language. Here’s a quick primer: