So my character (a level 10 human enchanter wizard) was tasked with infiltrating the home of a mysterious elf to steal a maguffin. The elf employs around 10 guards on varying shifts, a house steward, and a captain of the guard. My plan is to use charm person/dominate person to get in and find the captain or steward, and use those spells to have them retrieve the item for me.
My concern is that while I'm casting a spell on one of the guards, some of the others will hear the voice and raise the alarm.
About Verbal Component: 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 of spoiling any spell with a verbal component that he tries to cast. (Emphasis mine)
My question is: how loudly must one speak to fulfill the requirement? And secondly, how far away can someone hear the sound(given unobstructed terrain outside with clear weather). Or perhaps, what would be the formula to calculate the perception dc to hear?
As a secondary note, the grounds of the estate lie near the center of a town in the middle of a harvest festival. Given festivities, how far away could one hear the sound of a spell?