  Extended Theories of Gravity are considered as a new approach for solving the
infrared and ultraviolet scale problems of the Standard Theory of Gravity
(General Relativity). Observational evidence of gravitational waves and
subsequent identification of the number of existing polarizations are an
effective tool for testing general relativity and extended theories of gravity.
The Newman-Penrose method is used to characterize the polarization modes for
specific forms of $ f(R) $ in the present study. Both the forms of the $ f(R) $
theory belong to a far more general variational class of gravitational waves,
capable of presenting up to six separate polarizations states. We have
introduced new $ f(R) $ gravity models as an attempt to have a theory with more
parametric regulations so that the model can be used to describe existing
issues and discover different directions in gravity physics. The primary goal
of this research is to look into the properties of gravitational waves with new
cases. The model shows the existence of scalar degrees of freedom in $ f(R) $
gravity metric notation.
