Chazal said we should make fast days when certain bad things happened. During these days the posuk speaks about blowing the shofar so the people would repent.

On fast days you should use a male ram’s horn which is bent. In the Bais Hamikdash the mouthpiece was covered with silver. Also there were two shofars and two trumpets on either side. The sound of the shofar should be shorter then the trumpets since the major mitzvah is the trumpets.

Rosh Hashana 3:5

There is a biblical mitzvah to blow the shofar on Yom Kippur of a Yovel [50^th] year.

This shofar blowing is done the same way as that of Rosh Hashana and the brachos of Mussaf on that day are the same as the nine brachos in the musaf of Rosh Hashana. R’ Yehuda says on Rosh Hashana you use a shofar of a male ram and on Yovel a wild goat’s horn.