Abstract The standard model of particle physics is known to be intriguingly successful. However, their rich phenomena represented by the phase transitions (PTs) have not been completely understood yet, including the possibility of the existence of unknown dark sectors. In this paper, we investigate the measurement of the equation of state parameter w and the sound speed of the PT plasma with the use of the gravitational waves (GWs) of the universe. Though the propagation of GW is insensitive to in itself, the sound speed value affects the dynamics of primordial density (or scalar curvature) perturbations, and the induced GW by their horizon reentry can then be an indirect probe both w and . We numerically reveal the concrete spectrum of the predicted induced GW with two simple examples of the scalar perturbation spectrum: the monochromatic and scale-invariant spectra. In the monochromatic case, we see that the resonant amplification and cancellation scales of the induced GW depend on the values at different times respectively. The scale-invariant case gives a more realistic spectrum and its specific shape will be compared with observations. In particular, the QCD phase transition corresponds with the frequency range of the pulsar timing array (PTA) observations. If the amplitude of primordial scalar power is in the range of 10 -4  ≲ A ζ  ≲ 10 -2 , the induced GW is consistent with current observational constraints and detectable in the future observation in Square Kilometer Array. Furthermore, the recent possible detection of stochastic GWs by NANOGrav 12.5 yr analysis 1 can be explained by the induced GW if A ζ  ∼ √(7) × 10 -3 .