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We present radio observations of two well-known double-double radio galaxies,J0041+3224 and J1835+6204, at frequencies ranging from 150 to 8460 MHz, usingboth the Giant Metrewave Radio Telescope and the Very Large Array. Theseobservations, over a large radio frequency range, enable us to determine thespectra of the inner and outer lobes. Our detailed spectral ageing analysis oftheir inner and outer lobes demonstrates that the outer doubles ofdouble-double radio galaxies are created by the previous cycle of activity,while the inner doubles are due to the present cycle of activity. The (coresubtracted) spectra of the inner doubles of both sources are power laws over alarge frequency range. We found that the duration of the quiescent phase ofJ0041+3224 is between 4 and 28 per cent of the active phase of the previousactivity. The outer north-western lobe of J1835+6204 has a compact hotspot andthe regions of both the outer hotspots have close to power-law (rather thancurved) spectra, which indicates that the outer lobes are still fed by jetmaterial ejected in the previous episode just before the central engine stoppedpowering the jet. We estimate that the duration of the quiescent phase ofJ1835+6204 is $\lapp$5 per cent of the duration of the active phase of theprevious activity. Therefore, we conclude that the duration of the quiescentphase can be as short as a few per cent of the active phase in radio galaxiesof this type.

Rejuvenated radio galaxies J0041+3224 and J1835+6204: how long can the quiescent phase of nuclear activity last?