field. In the most studied example, the Brans–Dicke (BD) theory [@BD61], the scalar field was massless but recently the massive scalar fields have been investigated for a potential role they can play in the early and late time cosmology and in astrophysics [@YPC12], [@ABWZ12] [@Jac99]. It was also recognized that Brans–Dicke theory with the BD parameter $\omega_{BD}$ equals to zero contains as a a subclass the so called extended theories of gravity with gravitational action defined by some function $f(R)$ of the scalar curvature [@SF2010], [@FT2010]. In both those theories matter fields are coupled minimally to the tensor field $g_{\mu\nu}$. Dynamics of the metric field however differs from the dynamics in GR due to the nontrivial interaction of the metric with the scalar field in the ST theories and due to the modified field equations in the case of extended theories. For the gravitational waves this shows up as an additional, in general massive, spin $0$ mode of the wave that potentially can be detected by interferometers. Gravitational waves were also studied in other generalized theories. Recently an exact plane wave solution was found in [@Bab12] for a class of Horndeski theory [@Horn74] which can be considered as a generalization 