  It is widely known that bouncing models with a dust hydrodynamical fluid
satisfying ${c_s^2=p_d/\rho_d\approx 0}$, where $c_s, p_d, \rho_d$ are the
sound velocity, pressure and energy density of the dust fluid, respectively,
have almost scale invariant spectrum of scalar perturbations and negligible
primordial gravitational waves. We investigate whether adding another fluid
with $1/3 < \lambda = p/\rho < 1$, which should dominate near the bounce, can
increase the amplitude of gravitational waves in the high frequency regime,
turning them detectable in near future observations for such range of
frequencies. Indeed, we show that the energy density of primordial
gravitational waves is proportional to $k^{2(9\lambda-1)/(1+3\lambda)}$ for
wavelengths which become bigger than the Hubble radius when this extra fluid
dominates the background. Hence, as $\lambda \to 1$ (an almost stiff matter
fluid), the energy density of primordial gravitational waves will increase
faster in frequency, turning them potentially detectable at high frequencies.
However, there is an extra factor $I_q(\lambda)$ in the amplitude which
decreases exponentially with $\lambda$. The net effect of these two
contributions turns the energy density of primordial gravitational waves not
sufficiently big at high frequencies in order to be detected by present day or
near future observations for models which satisfy the nucleosynthesis bounds
and is symmetric with respect to the bounce. Hence, symmetric bouncing models
where the background is dominated by a dust hydrodynamical fluid with small
sound velocity, do not present any significant amount of primordial
gravitational waves at any frequency range compatible with observations, even
if there are other fields present in the model dominating the bounce phase. Any
detection of such waves will then rule out this kind of models.
