  We consider a population of small, high-velocity cosmic string loops. We
assume the typical length of these loops is determined by the gravitational
radiation scale and use the results of \cite{Polchinski:2007rg} which pointed
out their highly relativistic nature. A study of the gravitational wave
emission from such a population is carried out. The large Lorentz boost
involved causes the lowest harmonics of the loops to fall within the frequency
band of the LIGO detector. Due to this feature the gravitational waves emitted
by such loops can be detected in a periodic search rather than in burst or
stochastic analysis.
  It is shown that, for interesting values of the string tension
($10^{-10}\lsim G\mu\lsim 10^{-8}$) the detector can observe loops at
reasonably high redshifts and that detection is, in principle, possible. We
compute the number of expected observations produced by such a process. For a
10 hour search we find that this number is of order $O(10^{-4})$. This is a
consequence of the low effective number density of the loops traveling along
the line of sight. However, small probabilities of reconnection and longer
observation times can improve the result.
