  We study the confinement/deconfinement phase transition of the radion field
in a warped model with a polynomial bulk potential. The backreaction of the
radion on the metric is taken into account by using the superpotential
formalism, while the radion effective potential is obtained from a novel
formulation which can incorporate the backreaction. The phase transition leads
to a stochastic gravitational wave background that depends on the energy scale
of the first Kaluza-Klein resonance, $m_{\textrm{KK}}$. This work completes
previous studies in the following aspects: i) we detail the evaluation of the
radion spectrum; ii) we report on the mismatches between the thick wall
approximation and the numerical bounce solution; iii) we include a suppression
factor in the spectrum of sound waves accounting for their finite lifetime;
and, iv) we update the bound on $m_{\textrm{KK}}$ in view of the O3 LIGO and
Virgo data. We find that the forthcoming gravitational wave interferometers can
probe scenarios where $m_{\textrm{KK}} \lesssim 10^9$ TeV, while the O3-run
bounds rule out warped models with $10^4 \textrm{TeV} \lesssim m_{\textrm{KK}}
\lesssim 10^7$ TeV exhibiting an extremely strong confinement/deconfinement
phase transition.
