  Symmetric teleparallel gravity (STG) offers an interesting third geometric
interpretation of gravitation besides its formulation in terms of a spacetime
metric and Levi-Civita connection or its teleparallel formulation. It describes
gravity through a connection which is not metric compatible, however is torsion
and curvature free. We investigate the propagation velocity of the
gravitational waves around Minkowski spacetime and their potential
polarizations in a general class of STG theories, the so-called "newer general
relativity" class. It is defined in terms of the most general Lagrangian that
is quadratic in the nonmetricity tensor, does not contain its derivatives and
is determined by five free parameters. In our work we employ the principal
symbol method and the Newman-Penrose formalism, to find that all waves
propagate with the speed of light, i.e., on the Minkowski spacetime light cone,
and to classify the theories according to the number of polarizations of the
waves depending on the choice of the parameters in the Lagrangian. In
particular it turns out that there exist more theories than just the
reformulation of general relativity which allow only for two polarization
modes. We also present a visualization of the parameter space of the theory to
better understand the structure of the model.
