  AIMS: We wish to study the spectral dependence of the radio emission from
cosmic-ray air showers around 100 PeV (1017 eV). METHODS: We observe short
radio pulses in a broad frequency band with the dipole-interferometer LOPES
(LOFAR Prototype Station), which is triggered by a particle detector array
named Karlsruhe Shower Core and Array Detector (KASCADE). LOFAR is the Low
Frequency Array. For this analysis, 23 strong air shower events are selected
using parameters from KASCADE. RESULTS: The resulting electric field spectra
fall off to higher frequencies. An average electric field spectrum is fitted
with an exponential, or alternatively, with a power law. The spectral slope
obtained is not consistent within uncertainties and it is slightly steeper than
the slope obtained from Monte Carlo simulations based on air showers simulated
with CORSIKA (Cosmic Ray Simulations for KASCADE). One of the strongest events
was measured during thunderstorm activity in the vicinity of LOPES and shows
the longest pulse length measured of 110 ns and a spectral slope of -3.6.
CONCLUSIONS: We show with two different methods that frequency spectra from air
shower radio emission can be reconstructed on event-by-event basis, with only
two dozen dipole antennae simultaneously over a broad range of frequencies.
According to the obtained spectral slopes, the maximum power is emitted below
40 MHz. Furthermore, the decrease in power to higher frequencies indicates a
loss in coherence determined by the shower disc thickness. We conclude that a
broader bandwidth, larger collecting area, and longer baselines, as will be
provided by LOFAR, are necessary to further investigate the relation of the
coherence, pulse length, and spectral slope of cosmic ray air showers.
