The ruling for sending blessings upon the Prophet after the adhan
Question
What is the ruling for sending blessings upon the Prophet (peace and blessings be upon him) after the adhan?
Answer
A Sunnah
Invoking blessings upon the Prophet (peace and blessings be upon him) after the adhan (the call to prayer) is firmly established in the corpus of authentic hadiths. 'Abdullah Ibn 'Amr Ibn al-'As (may God be pleased with them both) narrated that he heard the Prophet (peace and blessings be upon him) say, "When you hear the mu`adhin (the person who makes the call to prayer) calling for prayer, repeat what he says and then invoke blessings upon me, because whoever does so will be earn a tenfold reward. Then beseech God to grant me al-Wasilah: it is a high rank in paradise fit for only one of God’s servants, and I hope to be that person. I will intercede for whoever asks that I attain al-Wasilah."
The manner of sending blessings upon the Prophet (peace and blessings be upon him) after the adhan
There is no text that obligates a single manner, audible or silent, for sending blessings upon the Prophet (peace and blessings be upon him); the matter is open and capacious. When God Almighty legislates a matter in a general way and it is possible to execute it in different ways, it must be left general and it is impermissible to restrict it to a certain manner without supporting proof.
There are reports that evince the [permissibility of] invoking blessings upon the Prophet (peace and blessings be upon him) audibly after the adhan. Abu al-Darda` (may God be pleased with him) narrated that after hearing the adhan, the Messenger (peace and blessings upon him) would say, "Allahuma Rab hadhihi ad-da'wah at-tama was-salat al-qa`imah, salli 'ala Muhammad wa a`tihu su`alihu yawm al-qiyamah [O God, Lord of this most perfect call and prayer that is now being established, send your blessings upon Muhammad and grant him his wish on the Day of Resurrection]." This was heard by those around him and they would repeat the mu`adhin's words. The Prophet (peace and blessings be upon him) said, "Whoever says this when he hears the mu`adhin, it becomes incumbent upon me to intercede for him on the Day of Judgment."
The ruling
The matter is open and the right thing to do is to let people behave naturally. Whoever wants to send blessings upon the Prophet (peace and blessings be upon him) is free to make it in the manner and words which best appeal to them since it is important that the manner and formula resonate in their hearts. It is impermissible for anyone to deny what others do as long as the matter is open and capacious.
And God Almighty knows best.