  The field equations of $f(R)$ gravity are rewritten in the form of obvious
wave equations with the stress-energy pseudotensor of the matter fields and the
gravitational field as its source under the de Donder condition. The method of
multipole analysis in terms of irreducible Cartesian tensors is applied to the
linearized $f(R)$ gravity, and its multipole expansion is presented explicitly.
In this expansion, the tensor part is symmetric and trace-free and is the same
as that in General Relativity, and the scalar part predicts the appearance of
monopole and dipole radiation in $f(R)$ gravity, as shown in literature. As a
by-product, the multipole expansion for the massive Klein-Gordon field with an
external source in terms of irreducible Cartesian tensors and its corresponding
stationary results are provided.
