First off, I'm not sure where you get the numbers in your equations. Your first one uses 2.83 volts, the second one uses 2 volts. The two equations aren't identical on any levels, they should only change in the impedance category which means resistance is halved.

In any event, I'll find the link where I asked a similar question and it was answered. Also, remember that we gain 3 db effeciency because the cone area doubles.

Adam