to and fro
adverb
[ ˌtuː ən ˈfrəʊ ]
• in a constant movement backwards and forwards or from side to side.
• "she cradled him, rocking him to and fro"
to and fro
verb
• move constantly backwards and forwards.
• "the ducks were toing and froing"
to and fro
noun
• constant movement backwards and forwards.
• "Wilkie watched the to and fro of their dancing"
Origin:
Middle English: fro from Old Norse frá (see from).