A baby waves ta-ta.
An example of ta ta is when you wave your baby's hand and have him say "ta ta" to daddy.
Origin of ta-taorigin, originally a child's term
Origin of ta-taOf baby-talk origin.
- (chiefly UK, Australia, New Zealand, informal, colloquial) Goodbye.
Dated and rarely used in The United States, sometimes used in Canada. Although likely to be understood, it is likely to be considered rather humorous, particularly if used in a parody of British English speakers.
Probably derived from baby talk c1823 (imitative).