Originally Posted by SRD/PHB p. 174
A verbal component is a spoken incantation. To provide a verbal component, you must be able to speak in a strong voice. A silence spell or a gag spoils the incantation (and thus the spell). A spellcaster who has been deafened has a 20% chance to spoil any spell with a verbal component that he or she tries to cast.
Unfortunately by RAW this does not say that you have to utter the verbal componenent in "a strong voice", you just have to be able to. So unless someone finds a different quote, it is up to the DM how loudly th everbal component must be spoken.