  We study the elastic signatures -- renormalisation of sound velocity and
magnetostriction -- of the spin-nematic phase of a spin-$1$ magnet on a
triangular lattice described by the bilinear-biquadratic spin Hamiltonian. We
show that at low temperatures, the scattering of the acoustic phonons from the
Goldstone modes of the nematic phase lead to a powerlaw renormalisation of the
fractional change in the sound velocity, $v$, as a function of temperature,
$T$, i.e. $\Delta v/v\propto T^3$ as opposed to the same in the high
temperature paramagnet where $\Delta v/v\propto T^{-1}$. At the generically
discontinuous nematic transition, there is a jump in magnetostriction as well
as $\Delta v/v$ along with enhanced $h^4$ dependence on the magnetic field,
$h$, near the nematic transition. These signatures can help positively
characterise the spin-nematic in general and in particular the realisation of
such a phase in the candidate material NiGa$_2$S$_4$.
