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The simple physics above assumes perfect transition of energy to a given soundwave.
A flat frequency response is more of the real world engineering/acoustics regarding a speaker. It measures frequency and amplitude(dB) of input to output. Where the ideal is a 1:1 transition of input to output. Whether that actually corresponds to the power draw of a given speaker is an engineering question. Physics without engineering considerations still follows the previous where higher frequency is higher energy at same amplitude.
If you think about it a tweeter at 15,000Hz is moving back and forth 15,000 times in 1s. A woofer at 40Hz is only moving 40 times in 1s. While each woofer movement is more air it is slow while the tweeter is less air but much faster. As to why more air for the woofer that delves into how soundwaves are generated and propagated. A longer wave needs more space to not be cut short.
OK then let me ask this: Why do bass notes (and more to the point, woofers) require so much more power for a given volume? Is it just the increased moving mass of the speaker and air?
If that's the case, then I suspect that @SheeEttin@lemmy.zip has got the right answer:
But I'm not sure. Yet.
To go into human voices more the vocal folds within the larynx are the primary method of human pitch control. Air moving over the vocal folds vibrates them resulting in sound. Control of vocal fold tightness or loosening by associated muscle is how we alter our pitch. Generally male vocal folds are longer, for lower pitch, while female vocal folds are shorter, for higher pitch (post-puberty hormones). Males also have larger lung capacity than females generally.
The main method of altering loudness is by forcing more air through the vocal folds, creating a larger amplitude vibration.
Diaphragms are not pushing air at constant pressure unless you're holding a note.
As I noted earlier bass is perceived as quieter at same amplitude due to how our ears are shaped and work, however, bass also travels farther it is able to be heard farther away with less dissipation because longer waves are less likely to "run into" other stuff.
The nose, pharynx, and mouth also act as resonators and articulation that further alter human sound.
For the engineering yeah it is probably just about moving more air, and more air has to be moved because it is a longer wave that needs to be created.