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 Cs2CuCl4 in its nearly one-dimensional regime and confirm the theoretical predictions, demonstrating that ultrasound can be used as a powerful probe of strong correlations in one dimension.