'wave-like' originates from English, specifically the word 'wave' combined with the suffix '-like', where 'wave' originally meant 'a moving ridge or surge' and '-like' meant 'similar to' or 'having the form of'.

'wave' comes from Old English 'wafian'/'wǣf' (to wave, a wave) and passed through Middle English as 'wave' to modern English; the suffix '-like' comes from Old English '-līc' meaning 'having the form of' and later became the productive modern suffix '-like'. Together they formed the compound adjective 'wave-like' (and variant 'wavelike').

Initially the components described motion or form related to waves; over time the compound retained that core sense and is now used generally to describe anything resembling waves in form, motion, or pattern.