  We calculate the gravitational radiation from a cusp of the chiral cosmic
strings as a function of the current on the string in the limit of small values
of the current. The smoothing of the cosmic string cusp due to the presence of
the superconducting current on the string leads to the different behavior of
the gravitational radiation from the cusp as compared with the
non-superconducting (ordinary) string. The difference between the gravitational
energy radiation from the chiral cusp and the ordinary one is proportional to
the value of the current on the string. It is shown that there is a
high-frequency cutoff in the spectrum of the gravitational radiation from the
chiral string. The frequency cutoff depends on the value of the string current.
This effect is crucial for the detection of gravitation wave bursts from cosmic
strings: the rather large current on the string would lower the amplitude of
the incoming signal.
