  Programmable materials hold great potential for many applications such as
deployable structures, soft robotics, and wave control, however, the presence
of instability and disorder might hinder their utilization. Through a
combination of analytical, numerical, and experimental analyses, we harness the
interplay between instabilities, geometric frustration, and mechanical
deformations to control the propagation of sound waves within self-assembled
soft materials. We consider levitated magnetic disks confined by a magnetic
boundary in-plane. The assemblies can be either ordered or disordered depending
on the intrinsic disk symmetry. By applying an external load to the assembly,
we observe the nucleation and propagation of different topological defects
within the lattices. In the presence of instabilities, the defect propagation
gives rise to time-independent localized transition waves. Surprisingly, in the
presence of frustration, the applied load briefly introduces
deformation-induced order to the material. By further deforming the lattices,
new patterns emerge across all disk symmetries. We utilize these patterns to
tune sound propagation through the material. Our findings could open new
possibilities for designing exotic materials with potential applications
ranging from sound control to soft robotics.
