In this week's Parsha - יִתְרוֹ - we have the first occurrence (AFAIK) of the Shofar blast announcing something.
בִּמְשֹׁךְ הַיֹּבֵל הֵמָּה יַעֲלוּ בָהָר. When you hear the long shofar sound, you may again climb the mountain.
Rashi points out that this was a divine Shofar blowing
ושופר של אילו של יצחק היה - in which case we understand how a few million people could hear it.
However, in various places in תנ"ך we see the Shofar being used for announcements; often to signal the end of a conflict. The shofar was sounded and the conflict ended. Somehow everybody heard it and put their weapons down.
E.g.: Shmuel-2 Ch. 2 18 verse 16:
וַיִּתְקַע יוֹאָב בַּשֹּׁפָר וַיָּשָׁב הָעָם מִרְדֹף אַחֲרֵי יִשְׂרָאֵל כִּי חָשַׂךְ יוֹאָב אֶת הָעָם
Yoav blew the shofar and the nation stopped chasing the Israelites, for Yoav spared the nation.
How did this work? How far can the sound of a Shofar travel - even if they had an entire group of Shofar blowers.
How did people know this was a genuine peace-blast and not some peace activist trying to end the war?
The most astounding case is in Shmuel-2 Ch. 15 verse 10:
וַיִּשְׁלַח אַבְשָׁלוֹם מְרַגְּלִים בְּכָל שִׁבְטֵי יִשְׂרָאֵל לֵאמֹר כְּשָׁמְעֲכֶם אֶת קוֹל הַשֹּׁפָר וַאֲמַרְתֶּם מָלַךְ אַבְשָׁלוֹם בְּחֶבְרוֹן
Avshalom sent spies to all the tribes with instructions that when they hear the Shofar blast they should announce that Avshalom was crowned in Hebron.
How would the blast travel, reliably, all over the country?