Besides, the Hammett equation plot refers to thermodynamic/kinetic data of reactions that involve substituted aromatic rings that may not always coincide with their bathochromic shift (e.g. halide aromatic substitution), neither with their vibrational behavior.
As a comparison example:
Assume the hypothetical nitration of phenyl azide, p-hydroxy-phenyl azide and p-nitro-phenyl azide. The rate and the direction of nitration will be different in each case, depending on the relative electron donating/attraction strength of azide group, compared with the neighbor one; but their UV bathochromic shift will be cumulative (if not conjugative), and with a strong IR band at ≈ 2150 cm-1 that corresponds to the azide group.
Furthermore, the strength of conjugation is also a question of bond angles, which can explain the decrease any electron withdrawing character of azide, when being out of plane.