Loudspeakers should not be used outside the mosque for the prayer
Question

Is it better for us to use the indoor loudspeakers for taraaweeh and tahajjud prayers, or to use the outdoor loudspeakers so that people in the streets and neighbouring houses can hear?.
Praise be to Allah.Outdoor loudspeakers should not be used for the prayer, whether that is for taraaweeh, tahajjud or any other prayers such as Fajr, Maghrib and ‘Isha’, because that leads to many negative consequences and causes disturbance to the neighbours of the mosque.
 Shaykh Ibn ‘Uthaymeen was asked: 
In recent times it has become very common for the imams of mosques to use outdoor loudspeakers, which are usually placed in the minaret and the volume is set very high. By doing this, some mosques disturb one another in the prayers in which Qur’aan is recited out loud, by using these loudspeakers for the recitation. What is the ruling on using loudspeakers for the prayers in which Qur’aan is recited out loud when the sound from the minaret will disturb other mosques? 
He replied: 
What you have mentioned about using loudspeakers on the minaret for the prayers in which Qur’aan is recited out loud is something that is not allowed, because it causes a lot of disturbance for the people in houses and other mosques nearby. Imam Maalik (may Allaah have mercy on him) narrated in al-Muwatta’ (178), from Sharh al-Zarqaani in Baab al-‘Aml fi’l-Qiraa’ah (How Qur’aan is to be recited) from al-Bayaadi Farwah ibn ‘Amr – may Allaah be pleased with him – that the Messenger of Allaah (peace and blessings of Allaah be upon him) went out to the people when they were praying, and their voices were loud in recitation, and he said: “ A worshipper is conversing with his Lord, so let him think about the One with Whom he is conversing. Do not raise your voices above one another when reciting Qur’aan.” 
Abu Dawood (1332) narrated, under the heading, “Raising the voice when reciting Qur’aan in night prayers” that Abu Sa’eed al-Khudri – may Allaah be pleased with him – said: The Messenger of Allaah (peace and blessings of Allaah be upon him) observed i’tikaaf in the mosque and he heard them raising their voices in reciting Qur’aan. He drew back the curtain and said: “Each of you is conversing with his Lord, so do not disturb one another, and do not raise your voices above one another in reciting Qur’aan – or in prayer.” Ibn ‘Abd al-Barr said: The hadeeths of al-Bayaadi and Abu Sa’eed are both sound and saheeh. 
These two hadeeths show that it is forbidden to raise one's voice in reciting Qur’aan in prayer to such an extent that it disturbs others, and that this is a nuisance and is forbidden. Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him) said in Majmoo’ al-Fataawa (23/61): No one has the right to raise his voice so much when reciting out loud that he disturbs others, such as other worshippers. 
In an answer he gave in al-Fataawa al-Kubra (1/350) he said: Whoever does anything that disturbs the people in the mosque, or does anything that will lead to that, should be stopped.  
With regard to the excuses offered by those who raise their voices, that may be answered in two ways: 
1 – The Prophet (peace and blessings of Allaah be upon him) forbade people to raise their voices above one another in reciting Qur’aan, and explained that this causes annoyance. It is well known that the believer has no option and cannot ignore the ruling of the Prophet (peace and blessings of Allaah be upon him). Allaah says (interpretation of the meaning): 
“It is not for a believer, man or woman, when Allaah and His Messenger have decreed a matter that they should have any option in their decision. And whoever disobeys Allaah and His Messenger, he has indeed strayed into a plain error”
[al-Ahzaab 33:36]
It is also well known that a believer should not put himself in a position where he causes disturbance or annoyance to his brothers. 
2 – The excuses that they give, even if they have some grounds, nevertheless are outweighed by the forbidden things that happen as a result of raising the voice, such as the following: 
(i)doing something that the Prophet (peace and blessings of Allaah be upon him) forbade, namely worshippers raising their voices above one another
(ii)Annoying other worshippers who can hear one, as well as others such as people who are studying or trying to memorize Qur’aan
(iii)Distracting members of congregations in neighbouring mosques from listening to the recitation of their own imam, which they are commanded to listen to.
(iv)Some of the worshippers in neighbouring mosques may end up following the imam who is raising his voice in rukoo’ and sujood, especially if they are in a big mosque with a large congregation which they could be confused by the voice of an imam that drowns out the voice of their own imam. We have heard of many such incidents.
(v)It may lead to some people becoming negligent about hastening to attend the mosque, because they can hear the prayer of the imam rak’ah by rak’ah, step by step, so they dawdle, thinking that the imam is at the beginning of the prayer, until they miss most or all of the prayer.
(vi)It may cause the people who are coming to the mosque to rush when they heard the end of the imam’s recitation, as we see happening. Thus they do something that the Prophet (peace and blessings of Allaah be upon him) forbade, i.e., rushing, because they hear this amplified voice.
(vii)There may be people in the houses who hear this recitation when they are engaged in some idle pursuits or idles talk, as if they are careless about the reciter. This is the opposite of what those who support raising the volume suggest, which is that many of the women in the houses will hear the recitation and benefit from it. This benefit may be achieved through listening to tapes with recordings of the recitation of skilled reciters.
With regard to the comment by those who support raising the volume that it may influence some people and make them come and pray, especially if the voice of the reciter is beautiful, this may be true, but it is a rare benefit that is outweighed by the harmful effects mentioned above. 
The basic principle on which there is consensus is that if there is a conflict between pros and cons, we must look and see which outweighs the other and judge accordingly. If they are equal, then warding off harm takes priority over bringing benefits. 
My advice to my Muslim brothers is to err on the side of caution and to be compassionate towards their Muslim brothers who are disturbed by their worship because of what they hear of these amplified voices that are so loud that the worshipper does not know what he is saying or what he should say in the prayer of du’aa’, dhikr and Qur’aan. 
I heard that a man was leading the prayers and was reciting the tashahhud, but nearby there was a mosque from which he could hear the recitation of the imam, and he started to repeat the tashahhud because he couldn’t hear himself think, so he made the prayer too long for himself and for the people behind him. 
Moreover, if they do this and stop amplifying the sound from the minarets, they will be showing compassion towards their brothers, in obedience to the words of the Prophet (peace and blessings of Allaah be upon him): “Do not raise your voices above one another in reciting Qur’aan,” and his words, “Do not disturb one another, do not raise your voices above one another in reciting Qur’aan.” There is no secret that the heart finds spiritual joy and contentment in obeying the commands of Allaah and His Messenger. 
He also said: 
There is no reason not to make an exception in the case of the Mosques in Makkah and Madeenah and the jaami’ mosques in which Friday prayers are held, because some of the worshippers may be outside the mosque and need to hear the voice of the imam. This is subject to the condition that the jaami’ mosques are not so close to one another that they would disturb one another. If that is the case then the loudspeakers on the walls of the mosques should be set up so that the khutbah and prayer can be heard, and the loudspeakers on the minarets should be turned off at that time, so that benefits may be achieved without disturbing others. 
See Majmoo’ Fataawa Ibn ‘Uthaymeen, 13/74-96.