Do basses exert more energy in talking than sopranos?

My friend and I were talking about power requirements in loudspeaker design and the fact that almost all of the power is required to drive the woofers and move lots of air.

Then he asked "do basses exert more energy talking or singing than sopranos?"

Or put another way, does a lower frequency voice need more power (energy) to achieve the same volume as a high voice?