  The investigation of the transverse effect of gravitational waves (GWs) could
constitute a further tool to discriminate among several relativistic theories
of gravity on the ground. After a review of the TT gauge, the transverse effect
of GWs arising by standard general relativity (called Einstein's GWs in this
paper) is reanalized with a different choice of coordinates. In the chosen
gauge test masses have an apparent motion in the direction of propagation of
the wave, while in the transverse direction they appear at rest. Of course,
this is only a gauge artefact. In fact, from careful investigation of this
particular gauge, it is shown that the tidal forces associated with GWs act
along the directions orthogonal to the direction of propagation of waves. In
the analysis it is also shown, in a heuristic way, that the transverse effect
of Einstein's GWs arises from the propagation of the waves at the speed of the
light, thus only massless GWs are purely transverse. But, because the physics
of gravitational waves has to be investigated by studing the tidal forces as
appearing in the geodesic deviation equation and directly in a laboratory
environment on Earth, an analysis of these tidal forces and of the transverse
effect in the frame of the local observer is also performed. After this, for a
further better understanding of the transverse effect, an example of a wave,
which arises from scalar tensor gravity, with both transverse and genuinely
longitudinal modes is given and discussed. In the example the connection
between the longitudinal component and the velocity of the wave will be
mathematical shown.
  At the end of this paper the review of the TT gauge is completed, recovering
the gauge invariance between the presented gauge and the TT one.
