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A first principles density functional based linear response theory (the socalled Density Functional Perturbation theory \cite{dfpt}) has been combinedseparately with two recently developed formalism for a systematic study of thelattice dynamics in disordered binary alloys. The two formalisms are theAugmented space recursion (ASR) and the Itinerant coherent potentialapproximation (ICPA). The two different theories (DFPT-ASR and DFPT-ICPA)systematically provides a hierarchy of improvements upon the earlier singlesite based theories (like CPA etc.) and includes non-local correlations in thedisorder configurations. The formalisms explicitly take into accountfluctuations in masses, force constants and scattering lengths. The combinationof DFPT with these formulation helps in understanding the actual interplay offorce constants in alloys. We illustrate the methods by applying to a fccFe$_{50}$Pd$_{50}$ alloy.Comment: 11 pages, 7 figures, 2 table

Phonons in disordered alloys: Comparison between augmented-space-based approximations for configuration averaging to integration from first principles