The blowing of the shofar is an injunction from Leviticus 23:24:
Speak unto the children of Israel, saying: In the seventh month, in the first day of the month, shall be a solemn rest unto you, a memorial proclaimed with the blast of horns, a holy convocation.
The shofar blast is a wakeup call, as described by Maimonides:
“Arise you who are fast asleep, and awaken you who slumber, search your deeds, repent, and be mindful of your Creator . . . ”
Note that there is no description of how the horns will blast. So a variety of customs are followed by Jewish communities around the world.
There are 3 customary calls: