According to Rav Saadiah Gaon the Almighty commanded us to sound the shofar on Rosh Hashana for these ten reasons:
1) Rosh Hashana corresponds to the first day of creation and the shofar proclaims the sovereignty of the Creator. We are obliged to coronate God as King on this day in the manner written by Dovid, “בַּחֲצֹצְרוֹת וְקוֹל שׁוֹפָר הָרִיעוּ לִפְנֵי הַמֶּלֶךְ ה', With trumpets and the sound of shofar, call out in the presence of the King, Almighty” (Psalms 48:6).
2) Rosh Hashana is the beginning of the Ten Days of Repentance and the shofar calls the people to amend their lives before the final judgment of Yom Kippur. It was customary for rulers to issue a final warning to their subjects before punishing them for violating their decrees. Similarly, the shofar represents God’s last warning to His people to repent.
3) The sounding of the shofar recalls the revelation of the Torah on Mount Sinai. The Torah was given to us amid blasts of the shofar, as it is written, “וְקוֹל שׁוֹפָר חָזָק מְאֹד,” the sound of shofar was most powerful” (Shemos 19:16), and the people accepted it saying “We will do and we will listen.”
4) The shofar brings to mind the warnings and exhortations of the prophets which are likened to the blasts of the shofar, as it is said, וְשָׁמַע הַשֹׁמֵעַ אֶת קוֹל הַשׁוֹפָר וְלֹא נִזְהָר וַתָּבוֹא חֶרֶב וַתִּקָּחֵהוּ דָמוֹ בְּרֹאשׁוֹ יִהְיֶה ... וְהוּא נִזְהָר נַפְשׁוֹ מִלֵט. He who hears the sound of the shofar and does not take warning, the sword come ands takes him away, his blood will be upon his own head ... but he who heeds warning will save his soul. (Yechezkel 33:4,5).
5) The shofar reminds us of the destruction of the Holy Temple which was destroyed amid the sounding of enemy trumpets, as it is said: כִּי קוֹל שׁוֹפָר שָׁמַעַתְּ נַפְשִׁי תְּרוּעַת מִלְחָמָה—“For you have heard the sound of the shofar, O my soul, the shouts of battle (Yirmiyahu 4:19); and when we hear the shofar on Rosh Hashana, we pray to God to restore the Temple to its former glory.
6) The shofar recalls the willingness of Yitzchak to be sacrificed on the altar in obedience to God’s command to Avraham. We pray that with the sounding of the shofar his great deed will be recalled by the Almighty as a source of merit to his descendents.
7) It is the nature of the shofar’s sound to arouse the heart to awe and reverence. Thus when we hear the shofar, we tremble and humble ourselves before the presence of God.
8) The shofar reminds us of the ultimate Day of Judgment, as it is said, “קָרוֹב יוֹם ה' הַגָדוֹל, קָרוֹב וּמַהֵר מְאֹד—יוֹם שׁוֹפָר וּתְרוּעָה” “The great day of Almighty is near, it is near and rapidly approaching—a day of the shofar and shouting” (Tzefanyah 1:14, 16).
9) The shofar inspires us with hope for the ultimate ingathering of our people and their deliverance from exile, as it is said, “וְהָיָה בַּיוֹם הַהוּא יִתָּקַע בְּשׁוֹפָר גָדוֹל וּבָאוּ הָאֹבְדִים בְּאֶרֶץ אַשׁוּר וגו' And it will be on that day that a great shofar will be sounded; and those who were lost in the land of Ashur ... will come and prostrate themselves before Adonoy on the holy mountain in Yerushalayim.” (Yeshaya 27:13)
10) The shofar reminds us of the future resurrection of the dead and it reaffirms our faith that God will revive the dead which will be heralded with the sounding of the shofar.
This Psalm (47) is recited seven times prior to the sounding of the Shofar. The Name, אלהים, which refers to God’s manifestation, as One Who rules with strict justice, appears in this psalm seven times. Thus we mention the Name אלהים forty-nine times as a prelude to the sounding of the Shofar. Our sages have said that there are forty-nine levels of spiritual impurity before one reaches the lowest depth, from which no salvation is possible. On the other hand, there are forty-nine ascending levels of intellectual sanctity which man can attain. In reciting this psalm we pray for the blast of the Shofar to arouse God’s mercy to overcome His manifestation of strict justice. We also pray for the sound of the shofar to inspire us to climb from the forty-ninth level of spiritual impurity, to rise to the forty-ninth level of sanctity.
לַמְנַצֵּֽחַ לִבְנֵי־קֹֽרַח מִזְמוֹר: כָּל־הָעַמִּים תִּקְעוּ־כָף הָרִֽיעוּ לֵאלֹהִים בְּקוֹל רִנָּה: כִּי־יְהֹוָה עֶלְיוֹן נוֹרָא מֶֽלֶךְ גָּדוֹל עַל־כָּל־הָאָֽרֶץ: יַדְבֵּר עַמִּים תַּחְתֵּֽינוּ וּלְאֻמִּים תַּֽחַת רַגְלֵֽינוּ: יִבְחַר־לָֽנוּ אֶת־נַחֲלָתֵֽנוּ אֶת גְּאוֹן יַעֲקֹב אֲשֶׁר־אָהֵב סֶֽלָה: עָלָה אֱלֹהִים בִּתְרוּעָה יְהֹוָה בְּקוֹל שׁוֹפָר: זַמְּרוּ אֱלֹהִים זַמֵּֽרוּ זַמְּרוּ לְמַלְכֵּֽנוּ זַמֵּֽרוּ: כִּי מֶֽלֶךְ כָּל־הָאָֽרֶץ אֱלֹהִים זַמְּרוּ מַשְׂכִּיל: מָלַךְ אֱלֹהִים עַל־גּוֹיִם אֱלֹהִים יָשַׁב | עַל־כִּסֵּא קָדְשׁוֹ: נְדִיבֵי עַמִּים| נֶאֱסָֽפוּ עַם אֱלֹהֵי אַבְרָהָם כִּי לֵאלֹהִים מָגִנֵּי־אֶֽרֶץ מְאֹד נַעֲלָה:
To the Chief Musician, A psalm of the sons of Korach. All peoples, clap hands! shout to God with the voice of joyous song. For Adonoy is Most High, awesome; a great King [is He] over all the earth. He subdues peoples under us, and nations under our feet. He chose for us our inheritance, the pride of Yaakov which He loves forever. God has ascended with a blast— Adonoy, with the sound of the shofar. Sing praises to God, sing praises; sing praises to our King, sing praises. For King of all the earth is God, sing praises [you who are] skillful. God has reigned over all nations, God is seated upon His holy throne. The nobles of the nations gathered the nation of the God of Avraham; for God has the power to shield the earth, He is greatly exalted.

