'wavy-grained' originates from English, specifically the words 'wavy' and 'grained', where 'wavy' ultimately derives from Germanic/Old English roots related to 'wave' (originally meaning 'a waving or undulating motion') and 'grained' comes from 'grain' (Old French 'grain', from Latin 'granum') where 'granum' meant 'seed' and 'grain' later came to mean 'texture, streak, or fiber (as in wood)'.

'wavy-grained' formed in Modern English as a compound of 'wavy' + past-participial adjective 'grained' (from 'grain'), combining the sense 'having waves' with 'having a grain pattern' to describe wood or a textured surface.

Initially the components referred separately to 'wave-like' and to 'grain/texture'; over time the compound came to be used specifically to describe wood (or similar materials) that has an undulating or rippled grain pattern, i.e. 'having a wavy grain'.