  We present the results of a new, comprehensive investigation of the radio
spectral index of the Crab Nebula supernova remnant. New data at 74 MHz are
combined with data at 327 MHz, 1.5 GHz and 5 GHz. In contrast to previous
claims, little spatial variation in the spectral index is seen. In particular,
between 327 MHz and 5 GHz we see no evidence of spectral steepening near the
edge of the nebula, the ``jet'' or the ionized filaments. The rms limits on any
spectral index variations in these regions amount to no more than 0.01. We
believe that earlier reports of large steepening were the result of correlator
bias and image registration problems. An elongated feature was detected
1\arcmin northwest of the pulsar which may be a continuation of the well-known
wisp-like structures seen closer to the center of the nebula. At 74 MHz, we see
for the first time evidence of free-free absorption by the thermal material in
the Crab Nebula's filaments. Apart from some possible renewed acceleration
occurring in the wisps, the dominant accelerator of relativistic electrons in
the Crab Nebula is the pulsar itself.
