  We calculate the radio frequency (RF) spectrum of fermionic atoms near a
narrow Feshbach resonance, explaining observations made in ultracold samples of
$^6\rm{Li}$ [E. L. Hazlett {\it et al.}, Phys. Rev. Lett. {\bf 108}, 045304
(2012)]. We use a two channel resonance model to show that the RF spectrum
contains two peaks. In the wide-resonance limit, nearly all spectral weight
lies in one of these peaks, and typically the second peak is very broad. We
find strong temperature dependence, which can be traced to the energy
dependence of the two-particle scattering. In addition to microscopic
calculations, we use sum rule arguments to find generic features of the
spectrum which are model independent.
