As we have learned (see daf 28), the fifth perek of Massekhet Sota is a collection of homiletic interpretations of a number of biblical passages. The thread that holds these interpretations together is the fact that they were all said bo ba-yom – “on that day” – which is to say, on the day that Rabbi Elazar ben Azarya was appointed to the position of nasi of the Sanhedrin (see Massekhet Berakhot 28a).
We find that bo ba-yom Rabbi Akiva taught that az yashir was sung responsively (i.e. Moshe recited a line and the people repeated it), while Rabbi Nehemya understood that Moshe would begin a passage and the people would complete it. This discussion leads to a statement brought in the name of Rabbi Yosei HaGelili:
When the Children of Israel climbed out of the sea onto dry land, natnu enehem lomar shirah – they wanted to sing a song of praise. What did they do? With the appearance of the Shehina (God’s presence), a child resting on his mother’s lap sat up and a baby nursing at his mother’s breast dropped it from his mouth to say – “this is my God and I will glorify Him”
Some explain that the emphasis on the children’s song can be understood from the opening words of Rabbi Yosei HaGelili’s statement – natnu enehem lomar shirah – which implies that they were not entirely certain that a song of praise was appropriate, given that their redemption came at the cost of the deaths of the entire Egyptian army. When they saw the spontaneous response of the children, however, it became clear to them that the adults were obligated in a similar response.