Saying du’aa’ so that people behind one or to one’s right or left may repeat it is something for which there is no basis in the actions of the Sahaabah (may Allah be pleased with them).
As for raising the voice in du’aa’, if that disturbs the people who are doing tawaaf or annoys them, then it is not allowed, because the Prophet (blessings and peace of Allah be upon him) said to his Companions, when he heard them reciting out loud when they were praying in the mosque: “Do not raise your voices over one another with the Qur’aan”, or he said “when reciting”. Hence we say to people who are doing tawaaf: Do not recite out loud and disturb the people; rather each person may offer whatever supplication he likes. Hence if these mutawwifs say to the people: Do tawaaf and say Takbeer at the Black Stone and say, “Rabbana aatina fi’l-dunya hasanah wa fi’l-aakhirah hasanah wa qina ‘adhaab al-naar (Our Lord, give us that which is good in this world and that which is good in the Hereafter, and protect us from the torment of the Fire),” [al-Baqarah 2:201], and say whatever du’aa’ you wish during the rest of tawaaf, and remember Allah, and recite Qur'aan, and make sure that the people understand that, this would be better and more beneficial to the people, because each person could call upon his Lord and ask for whatever he needs and understand the meaning of what he is saying. This is unlike what the mutawwifs do now of reciting du’aa’s which those who are behind them do not know, and if you were to ask these people who are saying du’aa’ behind the mutawwif about the meaning of the words they are saying, in most cases they would not know. If people were to call upon their Lord with supplications of which they know the meaning and can benefit from, that is better than this. End quote.
Majmoo’ Fataawa Ibn ‘Uthaymeen, 22/335, 337