  We obtain a set of exact gravitational wave solutions for the ghost free
bimetric theory of gravity. With a flat reference metric, the theory admits the
vacuum Brinkmann plane wave solution for suitable choices of the coefficients
of different terms in the interaction potential. An exact gravitational wave
solution corresponding to a massive scalar mode is also admitted for arbitrary
choice of the coefficients with the reference metric being proportional to the
spacetime metric. The proportionality factor and the speed of the wave are
calculated in terms of the parameters of the theory. We also show that a F(R)
extension of the theory admits similar solutions but in general is plagued with
ghost instabilities.
