We investigate the wave phenomena to a fluid-particle model described by the multi-dimensional compressible Euler/Navier-Stokes coupled with the Vlasov-Fokker-Planck equation (Euler-VFP or NS-VFP) through the relaxation drag force on the fluid momentum equation and the Vlasov force on the particle transport. We prove the globally nonlinear time-asymptotical stability of the planar rarefaction wave to 3D Euler-VFP system, which as we know is the first result about the nonlinear stability of basic hyperbolic waves for the multi-dimensional compressible Euler equations with low order dissipative effects (i.e., relaxation friction damping). This new (hyperbolic) wave phenomena comes essentially from the fluid-particle interactions through the relaxation friction damping, which is different from the interesting diffusive phenomena for either the compressible Euler equations with damping or the pure Fokker-Planck equation. Similar phenomena is also shown for 3D compressible NS-VFP, and it is further proved that as the shear and bulk viscosities tend to zero, the global solution to 3D compressible NS-VFP system around the planar rarefaction wave converges to that of 3D Euler-VFP system at the uniform rate with respect to the viscosity coefficients. This is joint work with Teng Wang (BJUT) and Yi Wang (AMSS) .