Spin waves (SW) are low energy excitations of magnetization in magnetic materials. In the promising field of magnonics, fundamental SW modes, magnons, are accessible in magnetic nanostructure waveguides and carry information. The SW propagates in both metals and insulators via magnetization dynamics. Energy dissipation through damping can be low compared to the Joule heating in conventional circuits. We performed simulations in a quasi-one-dimensional ferromagnetic strip and found that the transmission of the propagating SW across the domain wall (DW) depends strongly on the tilt angle of the magnetization at low frequencies. When the SW amplitude is large, the magnetization tilt angle inside the DW changes due to the effective fields. The SW transmission, the DW motion, and the magnetization tilt angle couple to each other, which results in complex DW motion and SW transmission. Both SW filtering and DW motions are key ingredients in magnonics.