We present a multi-frequency study of radio relics associated with the galaxy clusters A4038 , A1664 and A786 .
Radio images , integrated spectra , spectral index maps and fits to the integrated spectra in the framework of the adiabatic compression model are presented .
Images of the relic in A4038 at 150 , 240 and 606 MHz with the GMRT have revealed extended ultra-steep spectrum ( \alpha \sim - 1.8 to -2.7 ) emission of an extent 210 \times 80 kpc ^ { 2 } .
The model of passively evolving radio lobes compressed by a shock best fits the integrated spectrum .
The relic with a circular morphology at the outskirts of the cluster A1664 has an integrated spectral index of \sim - 1.10 \pm 0.06 and is best fit by the model of radio lobes lurking for \sim 4 \times 10 ^ { 7 } yr .
The relic near A786 has a curved spectrum and is best fit by a model of radio lobes lurking for \sim 3 \times 10 ^ { 7 } yr. At 4.7 GHz , a compact radio source , possibly the progenitor of the A786 relic , is detected near the center of the radio relic .
The A786 radio relic is thus likely a lurking radio galaxy rather than a site of cosmological shock as has been considered in earlier studies .