  We study the relative contribution of cusps and pseudocusps, on cosmic
(super)strings, to the emitted bursts of gravitational waves. The gravitational
wave emission in the vicinity of highly relativistic points on the string
follows, for a high enough frequency, a logarithmic decrease. The slope has
been analytically found to be $^{-4}/_3$ for points reaching exactly the speed
of light in the limit $c=1$. We investigate the variations of this high
frequency behaviour with respect to the velocity of the points considered, for
strings formed through a numerical simulation, and we then compute numerically
the gravitational waves emitted. We find that for string points moving with
velocities as far as $10^{-3}$ from the theoretical (relativistic) limit $c=1$,
gravitational wave emission follows a behaviour consistent with that of cusps,
effectively increasing the number of cusps on a string. Indeed, depending on
the velocity threshold chosen for such behaviour, we show the emitting part of
the string worldsheet is enhanced by a factor ${\cal O}(10^3)$ with respect to
the emission of cusps only.
