WITH HAND [I] › to raise your hand and move it from side to side in order to attract someone's attention or to say goodbye: Wave goodbye to Grandma. She waved at him.
wave sb in/on/through, etc › to show which way you want someone to go by moving your hand in that direction: The police waved him on.
MOVE SIDE TO SIDE [I, T] (also wave about/around) › to move from side to side in the air or make something move this way: The long grass waved in the breeze. He started waving his arms about wildly.