Most of the power in music is in the low frequencies. The speaker's "power requirements" don't change. How much power you need to drive the higher frequencies depends on where you cross-over. I'd guess that amps handling 100 Hz & up can be a quarter or half the power of whatever the speaker's "requirements" are. The speaker manufacturer's upper limit should be regarded as a safety spec. Exceeding that power could damage the speaker. There is no lower limit. You don''t lose sleep because you music system is turned off, do you? Happy listening.
Speaker relative efficiency/sensitivity when using a high pass filter
Is there a formula/algorithm/rule of thumb for calculating how a speaker's power requirements might change when the lower frequencies are handled by a subwoofer? Specifically for a ported speaker with a supposed frequency response down to 35Hz and an a 89dB sensitivity with a second order crossover at 80Hz. I know it goes down but by how much? I recognize that power requirements increase as frequency decreases but is the difference enough to allow for a less powerful amp? I would think so.