  In the framework of black hole perturbation theory, this work investigates
the standing wave solutions in Reissner-Nordtsr\"om (RN) anti-de Sitter (AdS)
spacetimes with a naked singularity. These solutions can be viewed as a
specific class of quasinormal modes exhibiting distinct characteristics. The
imaginary parts of their frequencies are numerically vanishing, allowing them
to persist over an extended period. Besides, these modes are predominantly
stationary in terms of the evolution of spacetime waveforms. The numerical
calculations are carried out employing the finite difference method, and the
quasinormal frequencies extracted by the Prony method are shown to be
consistent with those obtained using the matrix method. The obtained waveforms
and quasinormal frequencies are shown to be drastically different from those of
an extreme RN-AdS black hole. As the quasinormal modes are primarily
dissipative, the non-dissipative standing waves are attributed to the nature
that the singularity can neither be a sink nor a source of the gravitational
system.
