  We have studied scalar, electromagnetic and gravitational perturbations of
the four-dimensional Reissner-Nordstr\"{o}m-like black holes with a
\textit{tidal charge} in the Randall-Sundrum braneworld. The quasinormal modes
of these scalar, electromagnetic, as well as axial and polar gravitational
perturbations, have been studied in both normal and eikonal regimes.
Calculations have shown that the black holes on the Randall-Sundrum brane are
stable against scalar, electromagnetic and gravitational perturbations.
Moreover, we determine the grey body factor, giving transmission and reflection
of the scattered waves through the scalar, electromagnetic and gravitational
effective potentials. It has been shown that the scalar perturbative fields are
the most favorite to the reflected as compared to the latter. With increasing
value of the tidal charge ability of the all perturbative potentials to reflect
the waves decreases. Our calculations in low- and high-frequency regimes have
shown that black holes on the braneworld always have a bigger absorption cross
section of massless scalar waves than the Schwarzschild and standard
Reissner-Nordstr\"{o}m black holes.
