"Play back and forth" is a phrase often used to describe a rhythmic action of movement or communication between two people or objects. However, there are various synonyms that can be used in place of this phrase, depending on the context. These synonyms include "alternate," "exchange," "move to and fro," "pass to and fro," "swing," "switch," and "trade." These synonyms can be used in a variety of situations, such as in games, sports, conversations, and music. Using different synonyms can help to add variety and interest to writing and communication, making it more engaging and effective.