Or HaChaim on Exodus 15:1/אור החיים על שמות ט״ו:א׳

1 אז ישיר משה, Then Moses began to sing, etc. It would have sufficed for the Torah to write וישר משה, "Moses sang," without the introduction אז, "then." However, the Torah wanted to tell us of the preparation which resulted in that song of jubilation. After Israel acquired the fear of G'd's Majesty, which in turn resulted in a profound measure of faith both in G'd and in Moses, they were divinely inspired to sing this song of thanksgiving.

2The reason the Torah writes ישיר "will sing," instead of שר, sang, something that would be so much more appropriate with the word אז is, that to this day we sing this song daily in our morning prayers. Had the Torah written אז שר משה, we would have assumed that the song was appropriate only for the people who had been present when the sea was split.

3ויאמרו לאמור, אשירה, they said saying: "I will sing, etc." This means that the Israelites said this to one another. The idea was that they wanted to coordinate their song; they did not want each one to use his own formulation. The fact that they succeeded in this is reflected in the singular "I will sing!"

4כי גאה גאה, for He has triumphed gloriously, etc. As a rule songs of praise should commence with mention of the collapse of G'd's enemies similar to what Solomon said in Proverbs 11,10: ובאבוד רשעים רנה "when the wicked perish there is jubilation." Accordingly, we understand the words גאה גאה as referring to Pharaoh who was so boastful that his very name was "the boastful one." Normally, boastful people consider themselves superior to their peers. Inasmuch as their peers do not amount to much, neither does their own pride. Pharaoh was more presumptious than the average braggart, however, as he thought himself superior even to G'd. This is why Moses wrote גאה גאה, the braggart of all braggarts.

5We may also understand the expression as analogous to Psalms 93,1 "The Lord is king, He is robed in splendour." As long as G'd had not disposed of Pharaoh He was known simply as גאה, glorious; after G'd disposed of the braggart Pharaoh He assumed an additional dimension of glory, hence גאה גאה. The repetition of the expression גאה may also reflect that G'd is glorious both in the celestial and in the terrestrial spheres. This would explain why no additional subject is appended after the word ורכבו. We may also understand the verse as follows: "I will sing to the Lord because He has proven so glorious; the words כי גאה גאה may also be read together with the rest of the verse, i.e. "He has flung into the sea both the horse and its boastful rider."