Hidden Symmetries in Acoustic Wave Systems

Latent symmetries are hidden symmetries which become manifest by performing a reduction of a given discrete system into an effective lower-dimensional one. We show how latent symmetries can be leveraged for continuous wave setups in the form of acoustic networks. These are systematically designed to possess latent-symmetry induced pointwise amplitude parity between selected waveguide junctions for all low frequency eigenmodes. We develop a modular principle to interconnect latently symmetric networks to feature multiple latently symmetric junction pairs. By connecting such networks to a mirror symmetric subsystem, we design asymmetric setups featuring eigenmodes with domain-wise parity. Bridging the gap between discrete and continuous models, our work takes a pivotal step towards exploiting hidden geometrical symmetries in realistic wave setups.