Based on the Talmud Yerushalmi, the Reviah rules that the blessing before the mitzvah of shofar should end with the words לשמוע קול שופר.
However, according to the Rosh and Rabbenu Tam, the correct ending is על תקיעת שופר, “…to hear the blowing of the shofar,” much like the reading of Megilas Esther, when we say על מקרא מגילה.
However, the Behag explains that the reason we say לשמוע קול שופר rather than לתקוע בשופר or על תקיעת שופר is that the mitzvah is actually fulfilled by hearing the shofar, not necessarily playing the shofar.
In fact, the Mishnah discusses a case where the shofar blower is above ground and the listeners are in a pit. If they hear the shofar while he hears only the echo, they fulfill their obligation, but the shofar blower himself does not (Rosh Hashana 20b).
The Chayei Adam adds that this is reflected in the verse that is the source of the mitzvah, יום תרועה יהיה לכם. Here the verse does not command us to blow the shofar, but to have a day of תרועה. However, note that the Gemara does state that Hashem told us to blow the shofar: רחמנא אמר תקעו (Rosh Hashana 16b).