Rif Rosh HaShana 7b {Rosh haShana 28a continues; 28b - 29a}

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7b

{Rosh haShana 28a continues}
Rava said: One who vows off benefit from his friend, it is permitted to blow for him a shofar for mitzvah. And one who vows off benefit from a shofar, it is permitted to blow for him a blast of mitzvah. And one who vows of benefit from a spring, it is permitted for him to immerse an immersion of mitzvah in the rainy season {where he derives no benefit since it is cold and wet anyway} but not in the sunny season.

{Rosh haShana 28b}
They learnt {in a brayta}: If the listener intended and the one who made the sound did not intend, or the one who made the sound did not intend but the listener did not intend {to fulfill his obligation}, he did not fulfill, until both the listener and he who made the sound intended.

{Rosh haShana 29a}
Rabbi Zera said to his attendant: Intend and blow for me.
Thus it is clear that he holds that the one who makes the sound also requires intent.
That is to say, even though he {=the blower} intents to fulfill his own obligation, his fellow who hears him does not fulfill his obligation until the blower intends to sound it for him.
And these words are by an individual. But by the shliach tzibbur {agent of the congregation}, since his intent is to the entire world, we do not require that he has this one in mind specifically. As we learnt {in the Mishna}: If he was passing behind the synagogue, or his house was close to the synagogue, and he heard the sound of the shofar or the sound of the megillah, if he directed his heart he fulfilled and if he did not direct his heart, he did not fulfill.

Mishna:
A deaf-mute, an imbecile, and a minor cannot make the public fulfill their obligation {by blowing}.
This is the general rule: Anyone who is not obligated in the matter cannot make the public fulfill their obligation.

Gemara:
The Sages learnt {in a brayta}: All are obligated in blowing of shofar -- Kohanim, Levites, Israelites, converts, freed servants, tumtum {one whose gender is unknown because flesh covers it over}, androgynous people {who have both signs}, and one who is half servant and half free. An androgynous person can enable another of his type {=an androgynous pperson} to fulfill their obligation, but not one another type. A tumtum {who thus might be a tumtum male a tumtum female - we have know way of knowing} cannot enable either his own type or another type {since the other tumtum might be the other type of tumtum}.