  The energy budget for gravitational waves of a cosmological first order phase
transitions depends on the speed of sound in the thermal plasma in both phases
around the bubble wall. Working in the real-singlet augmented Standard Model,
which admits a strong two-step electroweak phase transition, we compute higher
order corrections to the pressure and sound speed. We compare our result to
lower-order approximations to the sound speed and the energy budget and
investigate the impact on the gravitational wave signal. We find that
deviations in the speed of sound from $c_s^2 = 1/3$ are enhanced up to
$\mathcal O(5\%)$ in our higher-order computation. This results in a
suppression in the energy budget of up to $\mathcal O (50\%)$ compared to
approximations assuming $c_s^2 = 1/3$. The effect is most significant for
hybrid and detonation solutions. We generalise our discussion to the case of
multiple inert scalars and the case of a reduced number of fermion families in
order to mimic hypothetical dark sector phase transitions. In this sector with
modified field content, the sound speed can receive significant suppression,
with potential order-of-magnitude impact on the gravitational wave amplitude.
