  In this paper we explore the possibility of observable gravitational waves as
a manifestation of the QCD axion dynamics. In particular, we focus on dynamical
axion models which solve the strong CP problem, and include the confinement of
a QCD-like gauge group at the TeV scale. We study the resulting chiral symmetry
breaking phase transition for models with $N_F=3$ and $N_F=4$ light flavors
using the linear sigma model. This model describes the scalar meson spectrum
and its interactions, with the diagonal field $\varphi$ as the order parameter.
We find that the amplitude of the gravitational wave spectrum depends on the
mass of the dynamical axion $\eta'$ via the ratio $m_{\eta'}/m_\varphi$. The
resulting spectra may be observed at future mid-range gravitational wave
experiments such as AION/MAGIS, DECIGO, and BBO. Moreover, the TeV states can
be searched for at colliders and their quantum numbers characterized, providing
a unique connection between axion physics, gravitational waves and collider
searches.
