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Radio relics are diffuse extended synchrotron sources that originate fromshock fronts induced by galaxy cluster mergers. The actual particleacceleration mechanism at the shock fronts is still under debate. The galaxycluster 1RXS J0603.3+4214 hosts one of the most intriguing examples of radiorelics, known as the Toothbrush. We present new wideband radio continuumobservations made with uGMRT and VLA. Our new observations, in combination withpreviously published data, allowed us to carry out a detailed high spatialresolution spectral and curvature analysis of the known diffuse radio emissionsources, over a broad range of frequencies. The integrated spectrum of theToothbrush follows closely a power law over close to 2 decades in frequency,with a spectral index of $-1.16\pm0.02$. We do not find any evidence ofspectral steepening below 8 GHz. The subregions of the Toothbrush show anidentical spectral slopes, suggesting that observed spectral index is ratherset by the distribution of Mach numbers which may have a similar shape atdifferent parts of the shock front. Indeed, numerical simulations show anintriguing similar spectral index, indicating that the radio spectrum isdominated by the average over the inhomogeneities within the shock, with mostof the emission coming from the tail of the Mach number distribution. Incontrast to the Toothbrush, the spectrum of the fainter relics show a highfrequency steepening. The integrated spectrum of the halo follows a power lawfrom 150 MHz to 3 GHz with a spectral index of $-1.16\pm0.04$. We do not findany evidence for spectral curvature, not even in subareas of the halo. Thissuggest a homogeneous acceleration throughout the cluster volume. Between thebrush region of the Toothbrush and the halo, the color-color analysis revealedemission that was consistent with an overlap between the two different spectralregions.

New mysteries and challenges from the Toothbrush relic: wideband observations from 550 MHz to 8 GHz