  The low-frequency radio spectra of the hotspots within powerful radio
galaxies can provide valuable information about the physical processes
operating at the site of the jet termination. These processes are responsible
for the dissipation of jet kinetic energy, particle acceleration, and
magnetic-field generation. Here we report new observations of the powerful
radio galaxy Cygnus A using the Low Frequency Array (LOFAR) between 109 and 183
MHz, at an angular resolution of ~3.5 arcsec. The radio emission of the lobes
is found to have a complex spectral index distribution, with a spectral
steepening found towards the centre of the source. For the first time, a
turnover in the radio spectrum of the two main hotspots of Cygnus A has been
directly observed. By combining our LOFAR imaging with data from the Very Large
Array at higher frequencies, we show that the very rapid turnover in the
hotspot spectra cannot be explained by a low-energy cut-off in the electron
energy distribution, as has been previously suggested. Thermal (free-free)
absorption or synchrotron self absorption models are able to describe the
low-frequency spectral shape of the hotspots, however, as with previous
studies, we find that the implied model parameters are unlikely, and
interpreting the spectra of the hotspots remains problematic.
