It may just be in a few cases, but in the case of a flute, a higher pitch appears to come with a perceived higher volume. Is this simply because you need to put more energy into the flute to get a higher harmonic? Why is that? It seems that one shouldn't need to put in more energy, and get a consequently a higher volume.
The physiology of human ear (and perhaps brain) makes sounds with frequency ~3000 Hz sound louder than higher and lower frequencies, for same sound wave pressure perturbation; see https://en.wikipedia.org/wiki/Equal-loudness_contour