אָש ִּירָ ה לַה' כִּּי גָאֹה גָּאָה...
Let me sing to Hashem for He has triumphed gloriously...
The Ohr Hachaim offers multiple explanations for the double expression גָאֹה גָאָה.
When a person acts with arrogance over another person, his arrogance is false. A human is frail and weak, lording over another human is lording over the weak. However, Par’oh was arrogant to Hashem, claiming “Who is Hashem that I should hearken his call?” This is true arrogance, and he needed to be degraded to the lowest level in return.
Another explanation is that the גָאֹה גָאָה is referring to Hashem. Hashem has a double triumph. Until now, Hashem was the ה מָלָךְ גֵאוּת לָבֵש – Hashem has reigned, clothed in triumph. Hashem was the only One who could act with justified arrogance. Now that He destroyed Par’oh, showing the world His supreme powers over the seemingly powerful, Hashem’s triumph was doubled.
Additionally, the Torah could be referring to Hashem’s double level of pride, both in the upper realms and the lower ones. Until now, the Mal’achim knew about how great Hashem was, and nobody up there dared rebel against Him. However, in this lower world, Hashem allowed humanity to rebel against Him, and the average bystander could not discern His tremendous powers in a universe filled with idol worshippers. Now that Hashem toppled the most powerful king of all, He showed them that in reality, He was the king of the entire universe, and his triumph is above all others, upper and lower.
However, the Ohr Hachaim acknowledges that these last two explanations fail to account for the continuation of the possuk, where the Torah talks about the horse and its rider. He suggests that the Torah has a double meaning, first, we are to read the possuk אָשִּירָה לַה' כִּי גָ אֹה גָאָה –I will sing to Hashem because He is doubly triumphant. This refers to the last two explanations. Then we can read it כִּי גָאֹה גָאָה סוּס וְרֹכְבוֹ רָמָה בַיָּם –For he was triumphant over the arrogant by hurling horse and rider into the sea.
