  We show that the third Goldstone mode in the two-species condensate mixtures,
which emerges at phase-separation, gets hardened when the confining potentials
have separated trap centers. The {\em sandwich} type condensate density
profiles, in this case, acquire a {\em side-by-side} density profile
configuration. We use Hartree-Fock-Bogoliubov theory with Popov approximation
to examine the mode evolution and density profiles for these phase transitions
at $T=0$.
