We demonstrate that any scaling source in the radiation era produces a background of gravitational waves with an exact scale-invariant power spectrum. Cosmic defects, created after a phase transition in the early Universe, are such a scaling source. We emphasise that the result is independent of the topology of the cosmic defects, the order of phase transition, and the nature of the symmetry broken, global or gauged. As an example, using large-scale numerical simulations, we calculate the scale invariant gravitational wave power spectrum generated by the dynamics of a global O(N) scalar theory. The result approaches the large N theoretical prediction as N^(-2), albeit with a large coefficient. The signal from global cosmic strings is O(100) times larger than the large N prediction.