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In this paper, 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 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 KK in view of the O3 LIGO and Virgo data. We find that the forthcoming gravitational wave interferometers can probe scenarios where m KK ≲ 1 0 9 TeV , while the O3-run bounds rule out warped models with 1 0 4 TeV ≲ m KK ≲ 1 0 7 TeV exhibiting an extremely strong confinement/deconfinement phase transition. [ABSTRACT FROM AUTHOR]