  We construct a many-body theory of magneto-elasticity in one dimension and
show that the dynamical correlation functions of the quantum magnet, connecting
the spins with phonons, involve all energy scales. Accounting for all magnetic
states non-perturbatively via the exact diagonalisation techniques of Bethe
ansatz, we find that the renormalisation of the phonon velocity is a
non-monotonous function of the external magnetic field and identify a new
mechanism for attenuation of phonons - via hybridisation with the continuum of
excitations at high energy. We conduct ultrasonic measurements on a
high-quality single crystal of the frustrated spin-1/2 Heisenberg
antiferromagnet $\textrm{Cs}_{2}\textrm{CuCl}_{4}$ in its one-dimensional
regime and confirm the theoretical predictions, demonstrating that ultrasound
can be used as a powerful probe of strong correlations in one dimension.
