The deaf wave their hands since clapping is moot.

You mean apart from waving your lighters (or cell phones, now) in the air at a concert?

Hello. This post has been removed as an example of a "throughout history" question, which is against the subreddit rules - here's the rule

If you are interested in a specific region/culture, feel free to re-post. Also, it would be useful to clarify the context: do you mean as a response to a performance (e.g. whistling, shouting 'Bravo', throwing flowers), or any form of appreciation (nodding, patting on the head, thumbs up, thanking, bowing, ..). Meanwhile, you may be interested in responses to similar questions (most of which break the same rule):

general

• Where did the common sign language used throughout the modern world (nodding, giving a thumbs up) originate?

clapping

• When did people start clapping to show appreciation?

• Is clapping/applause a "pre-historical" concept? Do we have evidence of it being written/drawn about and spread through cultures?

• How did the round of applause come into being?

• When did the act of applause become commonplace?

• How/when did clapping become an appropriate form of appreciation?

thumbs up

• Did Romans in the Colosseum really use the thumbs up/down? and if so, which was live and which was die?

• What's the deal with the "thumbs up" gesture?

• In Ancient Rome, did giving a "thumbs up" really signify to let someone live?