1. To wave one's hand back and forth in response to someone else. I waved back at the man, even though I had no idea who he was. The sight of my parents waving goodbye on the pier as my ship pulled away broke my heart, and I could barely remain composed enough to wave back.
2. To wave one's hand as a signal for someone or something to move back (from someone or something else). A noun or pronoun can be used between "wave" and "back." Several people started crowding around the injured man, so I waved them back to give him some space. A police officer stood in the road waving cars away from the scene of the accident.
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.
wave someone back (from something)
to motion someone to move back from something. The police officer waved the curious onlookers back from the scene of the crime. The students started to go onstage, but the teacher waved them back.
wave back (at someone)
to return someone's hand signal of greeting. I waved back at her, but she didn't see me. She didn't wave back.
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. © 2002 by The McGraw-Hill Companies, Inc.