In the Torah, Rosh Hashana is known as “Yom Terua”, the day of the Shofar blast. There is a debate among the rabbis in the Gemara as to what constitutes a Terua blast; some say it is three moderately-paced sounds, known as Shevarim, while others say it is nine blasts in rapid succession (which we call “Terua” nowadays). Still others say that a true Terua is the three blasts followed by the nine rapid ones. The Rishonim disagree whether the Shevarim and Terua are all done in the same breath or whether there is a pause between them. Furthermore, there is even disagreement among the Aharonim regarding the nature of doing it in one breath; the Hazon Ish says that the three blasts transition seamlessly into the nine, while the Mishna Berura (590:18) says that although they are all done in one breath, there is a slight pause between the two sets (listen to audio for examples). The Shulhan Aruch rules (O.H. 520:4) that, because there is disagreement in the matter, the blasts should be done in one breath during the seated Shofar ceremony, and in two breaths when it is blasted in the Musaf Amida. Some Moroccan communities follow the opinion of the Hazon Ish.
Summary: There are different opinions as to the sound of the Shofar blasts