  In this paper, we discuss the interaction of non-Abelian SU(2) Yang-Mills
progressive waves with gravitational waves. We solve and obtain some
interesting solutions to pure Yang-Mills equations in different backgrounds,
and perturbative solutions induced due to gravitational waves. These
perturbations show `beat patterns' and depending on boundary conditions,
changes in frequency. In flat space-time, when the Yang-Mills fields and the
gravitational waves are in the same direction there is no interaction, unless
there is self interaction of the Yang-Mills fields. In the system with non-zero
self interaction the amplitudes of the perturbation are inversely proportional
to the Yang-Mills coupling constant. In a cosmological background, the
Yang-Mills fields and the gravitational wave interact when they are in the same
direction even without self interaction of the Yang-Mills progressive fields.
We find that in the electroweak symmetry broken phase of the gauge fields, the
interactions are perturbative only for an infinitesimal time.
