'wavelike' is formed in Modern English by combining the noun 'wave' and the adjectival suffix '-like'. 'wave' originates from Old English (e.g. 'wafian' / 'wæf') and ultimately from Proto-Germanic '*waf-' meaning 'to wave' or 'a moving mass'; '-like' comes from Old English 'lic' meaning 'having the body or form of'.

'wave' developed from Old English words such as 'wafian'/'wæf' into Middle English 'wave' and then the modern English 'wave'; the suffix '-like' comes from Old English 'lic' and has been used since Old English to form adjectives. The combination 'wave' + '-like' produced 'wavelike' in Modern English.

Individually, 'wave' originally referred to a moving mass or the action of waving and '-like' meant 'having the form of'; when combined as 'wavelike' the meaning has remained essentially consistent as 'resembling a wave' or 'having wave characteristics'.