  The $1/r$-expansion in the distance to the source is applied to the
linearized $f(R)$ gravity, and its multipole expansion in the radiation field
with irreducible Cartesian tensors is presented. Then, the energy, momentum,
and angular momentum in the gravitational waves are provided for linearized
$f(R)$ gravity. All of these results have two parts which are associated with
the tensor part and the scalar part in the multipole expansion of linearized
$f(R)$ gravity, respectively. The former is the same as that in General
Relativity, and the latter, as the correction to the result in General
Relativity, is caused by the massive scalar degree of freedom, and places an
important role in distinguishing GR and $f(R)$ gravity.
