Sheikh `Abd al-`Azîz b. Bâz
As the questioner mentioned, during the time of the Prophet (peace be upon him) a single adhân was called as well as a single iqâmah. When the Prophet (peace be upon him) arrived to offer the sermon, one adhân was given. Then the Prophet (peace be upon him) offered the two sermons and the prayer was commenced with the calling of an iqâmah.
This is well known and is what is found in the Sunnah, like the questioner mentioned. This fact is something that the people of knowledge and faith are not heedless of.
During the era of the Caliph `Uthman b. `Affân, the population of Madinah grew enormously. He saw it best to introduce a second adhân. [Refer to Sahîh al-Bukhârî (912)]
The purpose of the first adhân was to draw the attention of the people to that fact that it was Friday so that they could prepare themselves and hurry to arrive at the mosque before the time of the regular adhân that was called after the Sun passed its zenith.
The other Companions who lived during his time followed him in that. This includes `Alî b. Abî Tâlib, `Abd al-Rahmân b. `Awf, al-Zubayr b. al-`Awwâm, and Talhah b. `Ubayd Allah, among other prominent Companions. The Muslims continued this practice in the majority of cities and countries following the precedent set by the Rightly Guided Caliph `Uthmân and upheld by the Rightly Guided caliph `Alî and all the other Companions.
This occurred during the reign of the third Rightly Guided Caliph and continued throughout the Muslim lands up to he present day. The Muslims did so following the Sunnah of the Caliph `Uthmân as a result of his ijtihâd in order to call the Muslims to righteousness.
There is nothing objectionable about their doing so, because the Prophet (peace be upon him) said: “You must adhere to my Sunnah and the Sunnah of the Rightly Guided Caliphs who come after me. Seize onto it with your molar teeth.” [Sunan al-Tirmidhî (2676), Sunan Abî Dâwûd (4607), Sunan Ibn Mâjah (42), and Musnad Ahmad (17142)]
`Uthmân and `Alî were both among the Rightly Guided Caliphs and we cannot doubt the clear and tangible benefit realized by calling the extra adhân.
Ahl al-Sunnah wa al-Jamâ`ah has upheld this practice without reservation, since in doing so they were following the Sunnah of these two Rightly Guided Caliphs as well as that of all the Companions who lived at that time.
[Majmû` Fatâwâ wa Maqâlât Mutanawwa`ah li-Salâhah al-Shaykh Ibn Bâz (12/347-349)]
Source: Islam Today