  We investigate gravitational waves generated in $f(Q,B)$ non-metric gravity,
i.e., a theory of gravity described by a non-metric compatible connection, free
of torsion and curvature. It is an extension of symmetric teleparallel gravity,
equipped with a boundary term $B$. This theory exhibits gravitational waves
regardless of the gauge adopted: they are the standard massless tensors plus a
massive scalar gravitational wave like in the case of $f(R)$ gravity. It is
precisely the boundary term $B$ that generates the massive scalar mode with an
effective mass $m_{B}$ associated to a Klein-Gordon equation in the linearized
boundary term. As in $f(Q)$ gravity also in $f(Q,B)$ non-metric gravity, a free
test particle follows a geodesic motion due to the covariant conservation with
respect to the Levi-Civita connection of the energy and momentum densities on
shell. Therefore, in $f(Q,B)$ gravity, the proper acceleration between two
neighboring worldlines traveled by two free point-like particle is governed by
a first-order geodesic deviation equation in the metric perturbation
$h_{\mu\nu}$. Thanks to this approximate linear equation, $f(Q,B)$ non-metric
gravity shows three polarization modes: two massless transverse tensor
radiation modes, with helicity equal to 2, reproducing the standard plus and
cross modes, exactly as in General Relativity, and an additional massive scalar
wave mode with transverse polarization of zero helicity. We obtain the same
result both by considering the coincidence gauge and by leaving the gauge free.
In summary, three degrees of freedom propagate in the $f(Q,B)$ linearized
theory with amplitudes $\tilde{h}^{(+)}$ and $\tilde{h}^{(\times)}$ for tensor
modes and amplitude $\tilde{h}^{(s)}$ for the scalar mode. Specifically, both
$f(Q,B)$ and $f(R)$ gravity involve the same massive transverse scalar
perturbation.
