Gemara

26b - Mishnah: On Rosh Hashanah we blow two trumpets, one on each side of the Shofar. The trumpets cease before the Shofar, because the Mitzvah today is the Shofar.

27a - Question: When there are two sounds at the same time, we cannot hear (either one)!

Beraisa: "Zachor" and "Shamor" were said simultaneously. A (human) mouth could not do this, and a (human) ear cannot hear it.

Answer #1: This is why the trumpets cease before the Shofar.

Inference: This shows that it suffices to hear the end of a Teki'ah (long Shofar blast), even if he did not hear the beginning. Likewise, it suffices to hear just the beginning.

Mishnah: Even if a Teki'ah was twice as long as is required, it counts only like one.

Question: Why don't we consider it like two blasts? (One can be Yotzei even without hearing the end of the first or the beginning of the second!)

Answer: We do not split a blast into two.

Question (Mishnah): If one blew into a pit or a big Keli he was Yotzei only if he heard the Shofar itself, but not if he heard the echo.

He should be Yotzei because he heard the beginning of the blast, before it merged with the echo!

Answer #2: Rather, two sounds from one source cannot be heard (like at Sinai), but if they come from two sources they can be heard.

Question (Beraisa): One person reads the Torah, and one translates. Two may not (simultaneously) translate (or read, for they will not be heard).

Answer: Our case is like the Seifa, which allows 10 people to recite Hallel or read the Megilah at the same time;

Since Hall and the Megilah are dear to people, they concentrate and can hear. The same applies to Shofar!

Rishonim

Rif (Megilah 12a): One person reads the Torah, and one translates. Two may not translate. Ten may read the Megilah at the same time. Since it is dear to people, they concentrate and can hear.

Rambam (Hilchos Tefilah 12:11): Two may not translate Torah at the same time. Rather, one reads and one translates.

Rosh (Megilah 3:1): Two may not read the Torah together. Rather, the Oleh reads but the Shali'ach Tzibur does not. Nowadays the custom is that the Shali'ach Tzibur reads. This is to avoid embarrassing people who cannot read. This is like Bikurim. At first, if one knew how to read he read. If he did not know how to read, others would be Makreh, i.e., they would read and he would repeat the words. People who did not know how to read were embarrassed and stopped bringing Bikurim. They enacted to be Makreh for everyone. This is not a good comparison. There, embarrassment stopped people bringing Bikurim altogether, and they transgressed mid'Oraisa. Here, the fluent people will read, and the others will be inspired to learn! Rather, some people do not know the cantillation and the Tzibur is not Yotzei. Such people might think that they know, and this is prone to lead to fights with the Shali'ach Tzibur. Therefore, it was enacted that the Shali'ach Tzibur read, for he is proficient. In any case, also the Oleh should read softly with the Shali'ach Tzibur, so his Berachah will not be l'Vatalah. One who does not know how to read should not be called. It is unreasonable that he bless and the Shali'ach Tzibur read.

Poskim

Shulchan Aruch (OC 141:2): Two may not read Torah at the same time. Rather, the Oleh reads and the Shali'ach Tzibur is quiet, or the Shali'ach Tzibur reads and the Oleh does not read aloud.

Mishnah Berurah (7): If the Oleh errs in the vowels or cantillation, the Shali'ach Tzibur helps him quietly.

Mishnah Berurah (8): Nowadays the Shali'ach Tzibur reads even when the Oleh is proficient. This is to avoid quarrels with people who think that they know, but in truth they err in the vowels and cantillation and cannot be Motzi the Tzibur.

Shulchan Aruch (ibid.): However, the Oleh must read with the Shali'ach Tzibur, so his Berachah will not be l'Vatalah. Rather, he reads inaudibly to himself.

Beis Yosef (DH u'Mah she'Chosav): In a Teshuvah, the Rosh says that it suffices if the Oleh can read along with the Shali'ach Tzibur. I.e., when he hears the Shali'ach Tzibur, he knows how to read the word from the Sefer Torah. Also many other Rishonim require every letter to be read from the Sefer. The Nimukei Yosef, Eshkol and Agudah permit a blind person to bless on Kri'as ha'Torah as long as someone else reads from it. They are the minority; we do not rely on them.

Rebuttal (Taz 3): The Yerushalmi (Megilah 4:1) cites an episode in which someone else blessed and R. Meir read. It permits, because Shome'a k'Oneh. This supports the Agudah. The Levush and Bach saw blind people get Aliyos, on condition that they are Chachamim.

Levushei Serad (6): The Yerushalmi discusses Kri'as ha'Megilah.

Beis Yosef (ibid.): Rav Sadya Gaon says that if a Kohen or Levi is needed and he cannot read, it suffices if he can read when the Shali'ach Tzibur is Makreh.

Question: Why is this necessary? The Kohen can pardon his honor and allow a great Chacham to read first!

Answer (Beis Yosef, ibid.): The case is, there is no such Chacham. Alternatively, the Kohen does not want to pardon his honor. Likewise, we do so for a Levi only if he does not agree to pardon his Zechus and allow the Kohen to read twice. Alternatively, perhaps it is better to Makreh a Kohen or Levi than for him to pardon his honor. We hold that a Kohen may not pardon his honor even on Monday and Thursday.

Beis Yosef (DH u'Mitoch): The Zohar says that it disgraces Torah if two people read at the same time. Even though Poskim say that it is a Berachah l'Vatalah if the Oleh does not read, since they have no source from the Talmud, they do not override the Zohar. Also, if the Oleh hears every word from the Shali'ach Tzibur and has intent, it is as if he said it, for Shome'a k'Oneh. Perhaps the Zohar allows the Oleh to read inaudibly to himself. Right before this, the Zohar said that Tefilah must not be audible to anyone else. It is proper to read inaudibly to himself.

Kaf ha'Chayim (16): The Ari would read softly; surely, he understood that the Zohar permits this. He read aloud only the Aseres ha'Dibros and Parashas Bechukosai.

Note: Presumably, the Aseres ha'Dibros are dear, so people concentrate and hear even if many read them. But why did he read Bechukosai aloud? If people are 'Ohev Es ha'Tochachos' (Avos 6:6), or concentrate well because the curses are dreadful, the same should apply to Ki Savo! Perhaps it is hard to concentrate for so long (there are 98 Klalos in Ki Savo, but only 49 in Bechukosai).

Beis Yosef (DH Benei): The custom in Rumania is for the Oleh to read aloud, like in the days of the Gemara. To avoid shame, the Shali'ach Tzibur is Makreh everyone. Rashi supports this. In Shabbos (12b) we learned that a Chazan may look at where children read (by light of a lamp) to review the beginnings of the Parshiyos. Rashi (DH Roshei) says that on Shabbos he quietly helps the Olim to read with the vowels and cantillation. Even though in Rumania the Shali'ach Tzibur reads aloud, since the Oleh reads after him, at any time there is only one voice. Perhaps even the Zohar would permit this.

Rema: Even if it is audible to himself we are not concerned, for it is no worse than Tefilah.

Gra (DH she'Lo): When a Shali'ach Tzibur reads aloud, the Zohar forbids the Oleh to read audibly to himself, just like regarding Tefilah. The Rema says that we are not concerned, because we hold (101:2) like the opinion that permits this regarding Tefilah.

Mishnah Berurah (12): It is better if he cannot hear himself.

Kaf ha'Chayim (18): The Rema argues with the Shulchan Aruch. The opinion of the Pri Chodosh is primary, that both in Kri'as ha'Torah and Tefilah one should not be able to hear himself.