  In this paper we calculate the speed of sound for three phases that may exist
inside a magnetized hybrid neutron star at different density regions: A
hadronic phase at low densities, quark-matter in the magnetic dual chiral
density wave (MDCDW) phase at intermediate densities and a free-quark phase
modeled by the MIT bag model at higher densities. It is found that the speed of
sound exhibits a non-monotonic behavior, that goes from values smaller than the
conformal limit ($c_s^2 < 1/3$) in the hadronic phase, to peak ($c_s^2 > 1/3$)
in the MDCDW phase, to finally reach the conformal limit ($c_s^2 \sim 1/3$) at
higher densities for quarks in the MIT bag model. Also, the anisotropic speed
of sound in the presence of a magnetic field is derived from first principles.
This is a consequence of the anisotropy in the system's pressures produced by
the breaking of the rotational symmetry in the presence of a magnetic field.
The role played by the lowest Landau level contribution in affecting the speed
of sound in the magnetized phases is discussed.
