  We present a new analysis of the widely used relation between cavity power
and radio luminosity in clusters of galaxies with evidence for strong AGN
feedback. We study the correlation at low radio frequencies using two new
surveys - the First Alternative Data Release of the TIFR GMRT Sky Survey (TGSS
ADR1) at 148 MHz and LOFAR's first all-sky survey, the Multifrequency Snapshot
Sky Survey (MSSS) at 140 MHz. We find a scaling relation $P_{\rm cav} \propto
L_{148}^{\beta}$, with a logarithmic slope of $\beta = 0.51 \pm 0.14$, which is
in good agreement with previous results based on data at 327 MHz. The large
scatter present in this correlation confirms the conclusion reached at higher
frequencies that the total radio luminosity at a single frequency is a poor
predictor of the total jet power. We show that including measurements at 148
MHz alone is insufficient to reliably compute the bolometric radio luminosity
and reduce the scatter in the correlation. For a subset of four well-resolved
sources, we examine the detected extended structures at low frequencies and
compare with the morphology known from higher frequency images and Chandra
X-ray maps. In Perseus we discuss details in the structures of the radio
mini-halo, while in the 2A 0335+096 cluster we observe new diffuse emission
associated with multiple X-ray cavities and likely originating from past
activity. For A2199 and MS 0735.6+7421, we confirm that the observed
low-frequency radio lobes are confined to the extents known from higher
frequencies. This new low-frequency analysis highlights the fact that existing
cavity power to radio luminosity relations are based on a relatively narrow
range of AGN outburst ages. We discuss how the correlation could be extended
using low frequency data from the LOFAR Two-metre Sky Survey (LoTSS) in
combination with future, complementary deeper X-ray observations.
