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We construct a simple analytical model to study the effects of cosmic strings on the microwave background radiation. Our model is based on counting random multiple impulses inflicted on photon trajectories by the string network between the time of recombination and today. We construct the temperature auto-correlation function and use it to obtain the effective power spectrum index n, the RMS-quadrupole-normalized amplitude Q sub RMS-PS and the RMS temperature variation smoothed on small angular scales. For the values of the scaling solution parameters obtained by Bennett and Bouchet [Phys. Rev D 41 (1990) 2408] and Allen and Shellard [Phys. Rev. Lett. 64 (1990) 119] we obtain n=1.14 plus or minus 0.5, Q sub RMS-PS = (4.5 plus or minus 1.5)G mu and (Delta T/T)sub RMS = 5.5 G mu. Demanding consistency of these results with the COBE data leads to G mu = (1.7 plus or minus 0.7) times 10 to the minus 6th (where mu is the string mass per unit length), in good agreement with direct normalization of mu from observations.
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