Rosh Hashanah marks the first day of the Ten Days of Repentance. We therefore sound the shofar as a means of announcing and warning that this period has begun. It is as if we announce: Those who choose to repent should do so now, and if they choose not to do so, let them not come later and complain about their fate. This too is the manner in which kings exercise their dominion, announcing their decrees to the accompaniment of trumpet blasts.