NOTE: The following is my own engineering reasoning only. It is extremely crude; use at your own risk. The below relates to perceived loudness only and has no bearing on sound quality.
Speakers make sound by moving air. The more air moved, the higher the sound pressure level & the higher the perceived loudness (but necessarily quality) of the sound.
Assumptions:
- The entire speaker driver moves proportionally to input power, P
- Speakers are perfectly efficient at all frequencies, converting all input power to driver displacement