Context :

Aims : We wish to study the spectral dependence of the radio emission from cosmic-ray air showers around 100 \leavevmode \nobreak \mathrm { PeV } ( 10 ^ { 17 } \leavevmode \nobreak \mathrm { 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 .
The radio data are digitally beam-formed before the spectra are determined by sub-band filtering and fast Fourier transformation .

Results : The resulting electric field spectra fall off to higher frequencies .
An average electric field spectrum is fitted with an exponential E _ { \nu } = K \cdot \mbox { exp } ( \nu / \mathrm { MHz } / \beta ) and \beta = -0.017 \pm 0.004 , or alternatively , with a power law \epsilon _ { \nu } = K \cdot \nu ^ { \alpha } and a spectral index of \alpha = -1 \pm 0.2 .
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 ) .
For the analyzed sample of LOPES events , we do not find any significant dependence of the spectral slope on the electric field amplitude , the azimuth angle , the zenith angle , the curvature radius , nor on the average distance of the antennae from the shower core position .
But one of the strongest events was measured during thunderstorm activity in the vicinity of LOPES and shows the longest pulse length measured of 110 \leavevmode \nobreak \mathrm { ns } and a spectral slope of \alpha = -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 .