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 _ { rms - PS } and the rms temperature variation smoothed on small angular scales .
For the values of the scaling solution parameters obtained in Refs . [ 10 ] , [ 3 ] we obtain n = 1.14 \pm 0.5 , Q _ { rms - PS } = ( 4.5 \pm 1.5 ) G \mu and ( { { \Delta T } \over T } ) _ { rms } = 5.5 G \mu .
Demanding consistency of these results with the COBE data leads to G \mu = ( 1.7 \pm 0.7 ) \times 10 ^ { -6 } ( where \mu is the string mass per unit length ) , in good agreement with direct normalizations of \mu from observations .