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.
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