The only thing Leviticus 23:24 says about this feast is to blow trumpets and memorialize it by not working, so it's designated as a holy holiday. In Bible times, there were many reasons why a shofar (ram's horn) was blown: to assemble the people, to go to war, or to announce the arrival or coronation of a king.
The first time we hear a shofar blown is when the Ten Commandments were given on Mount Sinai. GOD blew the trumpet and it made the people tremble! "Now Mount Sinai was completely in smoke because the Lord descended upon it in fire. Its smoke ascended like the smoke of a furnace, and the whole mountain quaked greatly. And when the blast of the trumpet sounded long and became louder and louder, Moses spoke, and God answered him by voice...Now all the people witnessed the thunderings, the lightning flashes, the sound of the trumpet and the mountain smoking; and when the people saw it, they trembled and stood afar off" (Ex. 19:18-19; 20:18). Recounting it later, Moses also speaks fire on the mountain (Deut. 5:4-5).
Psalm 29 describes the voice of the Lord vividly. It thunders, is powerful, full of majesty, breaks and splinters the cedars, and shakes and strips. As we take time to sit with the Lord on this His "appointed" day (Lev. 23:2), let us ask Him to blow His shofar over all walls and barriers in us and our loved ones and bring them down like He did the walls of Jericho--also with trumpet blasts (Josh. 6)--that we might follow Him with no hindrances as our hearts desire to.