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To signal with one's hand for someone or something to continue or proceed with their current course. A noun or pronoun can be used between "wave" and "on." The police officer waved us on as soon as the other cars had passed through the intersection. We need a team of volunteers to stand at certain parts of the race and wave on competitors so they don't get lost.
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.
wave someone or something on
to make a signal with the hand for someone or something to move on or keep moving. The traffic cop waved us on. The cop waved on the hordes of pedestrians.
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. © 2002 by The McGraw-Hill Companies, Inc.
To encourage or signal someone or something to proceed by or as if by waving the hand or arm: The police officer waved the pedestrians on. The crowd waved on the runners.
The American Heritage® Dictionary of Phrasal Verbs. Copyright © 2005 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.