The third out of five high holidays is the Day of Remembrance [of the trumpet sound]. This holiday has direct connection to the Tabernacle, and since it is coming up soon, I figured I would do a brief introduction.
The description of the most interest can be found in Numbers 10:1-10. Let's take a look:
1 And the LORD spake unto Moses, saying,
2 Make thee two trumpets of silver; of a whole piece shalt thou make them: that thou mayest use them for the calling of the assembly, and for the journeying of the camps.1 וַיְדַבֵּ֥ר יְהוָ֖ה אֶל־מֹשֶׁ֥ה לֵּאמֹֽר׃2 עֲשֵׂ֣ה לְךָ֗ שְׁתֵּי֙ חֲצֽוֹצְרֹ֣ת כֶּ֔סֶף מִקְשָׁ֖ה תַּעֲשֶׂ֣ה אֹתָ֑ם וְהָי֤וּ לְךָ֙ לְמִקְרָ֣א הָֽעֵדָ֔ה וּלְמַסַּ֖ע אֶת־הַֽמַּחֲנֽוֹת׃
As you can see, two special silver bugles (perhaps, horns or trumpets) were required to be made for the ceremonial purposes, as well as for practical purposes.
8 And the sons of Aaron, the priests, shall blow with the trumpets; and they shall be to you for an ordinance for ever throughout your generations.
9 And if ye go to war in your land against the enemy that oppresseth you, then ye shall blow an alarm with the trumpets; and ye shall be remembered before the LORD your God, and ye shall be saved from your enemies.
10 Also in the day of your gladness, and in your solemn days, and in the beginnings of your months, ye shall blow with the trumpets over your burnt offerings, and over the sacrifices of your peace offerings; that they may be to you for a memorial before your God: I am the LORD your God.
8 וּבְנֵ֤י אַהֲרֹן֙ הַכֹּ֣הֲנִ֔ים יִתְקְע֖וּ בַּֽחֲצֹצְר֑וֹת וְהָי֥וּ לָכֶ֛ם לְחֻקַּ֥ת עוֹלָ֖ם לְדֹרֹתֵיכֶֽם׃9 וְכִֽי־תָבֹ֨אוּ מִלְחָמָ֜ה בְּאַרְצְכֶ֗ם עַל־הַצַּר֙ הַצֹּרֵ֣ר אֶתְכֶ֔ם וַהֲרֵעֹתֶ֖ם בַּחֲצֹצְר֑וֹת וֲנִזְכַּרְתֶּ֗ם לִפְנֵי֙ יְהוָ֣ה אֱלֹֽהֵיכֶ֔ם וְנוֹשַׁעְתֶּ֖ם מֵאֹיְבֵיכֶֽם׃10 וּבְי֨וֹם שִׂמְחַתְכֶ֥ם וּֽבְמוֹעֲדֵיכֶם֮ וּבְרָאשֵׁ֣י חָדְשֵׁיכֶם֒ וּתְקַעְתֶּ֣ם בַּחֲצֹֽצְרֹ֗ת עַ֚ל עֹלֹ֣תֵיכֶ֔ם וְעַ֖ל זִבְחֵ֣י שַׁלְמֵיכֶ֑ם וְהָי֨וּ לָכֶ֤ם לְזִכָּרוֹן֙ לִפְנֵ֣י אֱלֹֽהֵיכֶ֔ם אֲנִ֖י יְהוָ֥ה אֱלֹהֵיכֶֽם׃ פ
As you can read from the last verses of this passage, the Sons of Aaron (Eleazar and Ithamar; the other two died) were assigned the task of these trumpets.
Since I have not researched this subject in details yet, I would have to leave my commentary on this as is for now. But I hope that in the future, I would be able to cover it more thoroughly.
One thing I would like to point out though:
In Jewish tradition this (holy)day is known as "Rosh HaShana" (aka Jewish New Year). This is incorrect, as in Leviticus 23:24-25 we are clearly told that the Day of Remembrance falls on the 1st day of the 7th month, and in Exodus 34:22 the seventh month is referred to as "the turning point" (autumn equinox) of the year (not "the end" of the year). Moreover, the term "Rosh HaShana" is explicitly used to indicate the 1st month (the month of Passover) in Exodus 12:2.
Here is a YouTube video that should give you an idea of the sound (but not necessarily shape) of these trumpets: