'wave' originates from Old English, specifically the word 'wafian,' where 'waf-' meant 'to move to and fro.'

'wafian' transformed into the Middle English word 'waven,' and eventually became the modern English word 'wave.'

Initially, it meant 'to move to and fro,' but over time it evolved into its current meaning of 'to move one's hand to and fro as a greeting or signal.'