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We report on micromagnetic simulation results of radiation of strong spin waves from the cores of magnetic vortices driven by their dynamics motion or the annihilation of a vortex-antivortex pair in a rectangular shaped magnetic thin film. Such strong spin-waves are distinguished from spin wave modes typically excited in patterned magnetic elements. The spin wave excitation with relatively low frequencies of 0–22 GHz are associated with the shape of an element, a magnetization configuration, and an applied magnetic field, while dominating spin waves in the higher frequencies of 22–96 GHz are driven by either the motion or annihilation of vortex cores present in the confined element. The latter case yields much higher amplitudes than the former does. It is found that large torques applied at the local area of the vortex cores, driven by the large exchange fields in the core region during their dynamic motion and collapse, induce a rapid energy dissipation into the surrounding areas through the spin-wave excitation and subsequent propagation. In addition, it is found that the strong spin waves radiated by the dynamic evolution processes of the vortex cores propagate well into a long stripe-shaped magnetic wire. Such traveling spin waves can be applicable for a new generation of magnetic logic devices.