Reference: Fataawa Noor ‘alad-Darb – Question No.6368, Page 200, Volume 12
Question: Is it a requirement that the words of remembrance are uttered audibly?
Response: It is sufficient to pronounce them with the tongue; [what is important is that] the words are uttered. As for repeating them in the heart, then this is insufficient.
However, there is an issue, and that is audibly uttering the words of remembrance after the obligatory prayers is [from the] Sunnah, as ‘Abdullaah ibn ‘Abbaas (radhi-yAllaahu ‘anhumaa) said that:
Ibn ‘Abbaas (radhi-yAllaahu ‘anhumaa) went on to say:
And many of the people nowadays have neglected this Sunnah, so you do not find them audibly [uttering the words of remembrance]; however, the truth is more deserving of being adhered to. So audibly [uttering the words of remembrance] is best, unless there is [a latecomer] praying next to you, and you fear that if you raised your voice it will disturb him, then here [our advice is] don’t raise your voice.