What are the connotations of 'Shirah'?
Targum Onkelos and Targum Yonasan: Shirah has connotations of thanks and praise (i.e., to sing the praises of).
When did Yisrael sing the Shirah?
Rashi (to Sotah 12b): On the twenty-first of Nisan. On the fifteenth, sixteenth and seventeenth, they had travelled from Ra'meses to Sukos... to Eisam and to Pi-ha'Chiros; on the eighteenth, Pharaoh was informed that the people had fled, on the nineteenth and twentieth the Egyptians chased after them. On the eve of the twenty-first they entered the Yam-Suf ,and on the morning of the twenty-first - which is synonymous with the last day of Pesach - they sang the Shirah.
Why does the Torah write "Az Yashir Moshe" (future)?
Rashi #1: What the Pasuk means is that, the moment Moshe saw the miracle, it entered his mind 1 to sing, 2 and that is what he proceeded to do. 3
Rashi #2 (citing the Mechilta): It refers to after Techiyas ha'Meisim. 4
Ramban: It is common for the Pasuk to speak in the future even when it is referring to the past. 5
Hadar Zekenim: To teach us that whoever sings Shirah in this world will merit to sing Shirah in the world to come.
Rashi: As we find regarding Yehoshua (10:12) and regarding the Song of the Well (Bamidbar 21:17 - See also Melachim I 7:8).
Rashi: Because the 'Yud' represents Machshavah.
On other occasions, the person concerned had in mind to do something, and did not put his thoughts into practice - see for example, Melachim I 11:7 (Rashi citing Sanhedrin 91b). The Ramban queries Rashi from a number of sources - See for example, Tehilim 106:19, 108:14 and from that entire chapter.
Rashi: This is one of the places where Techiyas ha'Meisim is hinted in the Torah. (See the opening Sugya in the last Perek of Sanhedrin). See also Torah Temimah, note 1.
The Ramban, who explains why the Torah does so, cites numerous examples of this (See for example, Shemos 33:7).
Why does the Torah use the doubled expression, "va'Yomeru Leimor"?
Ohr ha'Chayim: Each one prompted the other to sing, until they all sang in unison. 1
Chasam Sofer: To teach us that it is an obligation to recite the Shirah every day.
Sotah 30b: To teach us that Yisrael responded to Moshe, like one responds to the Chazan who recites Hallel. 2
What are the implications of the words "Ki Ga'oh Ga'ah"?
Rashi #1, Targum Onkelos and Targum Yonasan: It implies that Hashem was proud 1 over the proud ones. 2
Rashi #2: Doubled expressions refer to something that nobody else could possibly emulate. When one fights against a man riding a horse, he can only defeat him by toppling him from the horse, whereas Hashem cast the horse together with its rider into the sea.
Rashi #3: It implies that however much one praises Hashem, there are always more praises to add - in stark contrast to a human king, whose praises are undeserved.
Seforno: It implies that Hashem is deserving of praise for the goodness that He possesses, and not Pharaoh, who claimed that the Nile River was his and that he made himself.
Rashbam: The term 'Gei'us' is often used in connection with victory in war - as it does in this case. 3
Chagigah 13b: 'Sing to the One who is Proud over the proud ones' - The lion is king of the Chayos; the ox, of the Behemos; the eagle is king of the birds; man is king of all of them; and Ha'Kadosh-Baruch-Hu is King over them all and over the entire world.
Ramban: The horse is proud (vain) in battle, and the rider is proud over the horse (when he rides on its back), and Hashem was proud over both when He cast them together into the sea. See also answer #6.
Hashem does not tolerate people who are conceited before Him, and raises Himself above them and punishes them. Consequently, when Pharaoh, in his conceit, chased after Yisrael, He cast his horses together with their riders into the Yam-Suf and drowned them (Targum Yonasan).
See for example, Tehilim 94:2 and Tehilim 10:2.
Why does the Torah here write "Ramah ba'Yam" (which implies throwing upwards) and in Pasuk 15:4, "Yarah ba'Yam" (which implies casting downwards)?
Rashi: To teach us that the riders together with their horses were cast from the depths of the sea to the top and then down to the bottom again. 1
Why does the Torah write "Sus (singular) v'Rochevo"?
Rashi (to Bereishis 48:6): Because in the Eyes of Hashem , many horses are considered like one horse.
Seforno: It refers specifically to Pharaoh and his horse. 1
What are the implications of "Sus v'Rochevo Ramah ba'Yam"?
Rashi: It implies that Hashem cast the horse together with its rider up to the top, and down to the depths ("Yarah" - 15:4) - all while the rider was still attached to the horse.
What are the implications of the word "Az [Yashir Moshe]"?
Da'as Zekenim #1 and Hadar Zekenim #1: Moshe said to Hashem, 'I complained to You with the word 'Az' - 'u'me'Az Basi El Pharaoh;' 1 so I will praise You with the word 'Az' - 'Az Yashir Moshe.''
Da'as Zekenim #2 and Hadar Zekenim #2: The Gematriya of "Az" - eight - alludes to Bris Milah, which is on the eighth day, in the merit of which the sea split. 2
As the Pasuk writes in Tehilim, "L'Gozer Yam Suf li'Gezarim" (136:13); and Targum Onkelos translates the term "va'Yamol" (Bereishis 17:23) as 'u'Gezar.'
