  A good definition for the energy momentum tensor of gravity (EMTG) in General
Relativity (GR) is a hard, if not impossible, task. On the other hand, in its
teleparallel version, known as The Teleparallel Equivalent of General
Relativity (TEGR), one can define the EMTG in a very satisfactory way. In this
paper, it is proved that the EMTG of TEGR for linearized gravitational waves
(GWs) is the same as the version of GR that is usually given in the literature.
In addition, the exact version of the EMTG for a $pp-$wave with a $+$
polarization is obtained in a freely falling frame (FFF). Unlike the previous
case, the energy density can be either positive or negative, depending on the
details of the wave. The gravitational energy density for the Wyman spacetimes
is obtained both in a static frame and in a FFF. It turns out that observers in
free fall can measure the effects of gravity.
