posted by Sharon .
The minimum distance between particles in a wave that have the same displacement and are moving in the same direction is called?
Perhaps you need the Greek letter, Lambda
The question is poorly worded. For a planar wavefront, adjacent molecules in the same wave, in a direction perpendicular to wave travel, have the same displacement and direction.
So the wavelength is not the minimum distance between such particles or molecules.
Nevertheless, they are probably expecting the answer given by Damon.