Blazars are among the most powerful extragalactic objects, as a sub-class of active galactic nuclei. They launch relativistic jets and their emitted radiation shows strong variability across the entire electro-magnetic spectrum. The mechanisms producing the variability are still controversial and different models have been proposed to explain the observed variations in multi-frequency blazar light curves.We investigate the capabilities of the classical shock-in-jet model to explain and reconstruct the observed evolution of flares in the turnover frequency turnover flux density plane and their frequency-dependent light curve parameters. With a detailed parameter space study we provide the framework for future, detailed comparisons of observed flare signatures with the shock-in-jet scenario. Based on the shock model we compute synthetic single-dish light curves at different radio frequencies (2.6 to 345 GHz) and for different physical conditions in a conical jet (e.g. magnetic field geometry and Doppler factor). From those we extract the slopes of the different energy loss stages within the $ u_mathrm{m}$-$S_mathrm{m}$ plane and deduce the frequency-dependence of different light curve parameters such as flare amplitude, time scale and cross-band delays. The evolution of the Doppler factor along the jet has the largest influence on the evolution of the flare and on the frequency-dependent light curve parameters. The synchrotron stage can be hidden in the Compton or in the adiabatic stage, depending mainly on the evolution of the Doppler factor, which makes it difficult to detect its signature in observations. In addition, we show that the time lags between different frequencies can be used as an efficient tool to better constrain the physical properties of these objects.
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