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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.