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Volume is based on amplitude while frequency determines pitch.
Keeping frequency the same increasing amplitude is higher energy.
Keeping amplitude the same increasing frequency is higher energy.
So at the same volume(amplitude) a higher pitch(frequency) takes more energy.
The reason woofers have to move so much air is to increase amplitude of low frequency sounds. Humans generally perceive lower frequency as quieter, if a low and high pitch are at the same amplitude the higher pitch will be perceived as louder despite equal measurable volume due to audiological perception.
So does this question basically boil down to the following?
For a constant "perceived loudness", what does the plot of energy vs. frequency look like?
Once we know what the plot looks like, we could simply compare the bass and soprano regions.
I wondered about that at first, but then realized something: A good speaker has a flat frequency response, i.e. for a given input signal, it measures the same from bass to treble, against a 0dB reference. Does that correspond to power output, or...?