From how far can a verbal spell component be heard?

Question

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?

Answer 1

The perception rules give sample DCs. It is reasonable to equate "hearing someone speak in a strong voice" to "hear the details of a conversation" at DC 0. The DC increases by 1 for every 10 feet away, and a further +2 for the festivities (unfavorable conditions).

So if you try to dominate a guard who is patrolling 100 feet away from the nearest other guard, that nearest guard will need to succeed on a DC 12 check (+10 for 100 feet, +2 for background noise) to hear that something is going on. He would probably need to make an Intelligence check to realize that the noise was a spell being cast. If he doesn't know it was a spell, you could be long gone, and your new puppet can make up some reason like "Oh, I just stubbed my toe and cursed." Of course, the other guard would also be entitled to a Sense Motive check to determine traces of enchantment...

Note: By pure RAW, you do not need to actually speak in a strong voice, merely be able to, but you may have difficulty convincing your DM that it works this way.