  Gravitational wave observations provide unique opportunities to search for
cosmic strings. One of the strongest sources of gravitational waves is
discontinuities of cosmic strings, called kinks, which are generated at points
of intersection. Kinks on infinite strings are known to generate a
gravitational wave background over a wide range of frequencies. In this paper,
we calculate the spectrum of the gravitational wave background by numerically
solving the evolution equation for the distribution function of the kink
sharpness. We find that the number of kinks for small sharpness is larger than
the analytical estimate used in a previous work, which makes a difference in
the spectral shape. Our numerical approach also helps to avoid the use of
analytic approximations, and enables us to make a more precise prediction on
the spectral amplitude for future gravitational wave experiments.
