  A first principles density functional based linear response theory (the so
called Density Functional Perturbation theory \cite{dfpt}) has been combined
separately with two recently developed formalism for a systematic study of the
lattice dynamics in disordered binary alloys. The two formalisms are the
Augmented space recursion (ASR) and the Itinerant coherent potential
approximation (ICPA). The two different theories (DFPT-ASR and DFPT-ICPA)
systematically provides a hierarchy of improvements upon the earlier single
site based theories (like CPA etc.) and includes non-local correlations in the
disorder configurations. The formalisms explicitly take into account
fluctuations in masses, force constants and scattering lengths. The combination
of DFPT with these formulation helps in understanding the actual interplay of
force constants in alloys. We illustrate the methods by applying to a fcc
Fe$_{50}$Pd$_{50}$ alloy.
