Acoustic Analogues

The previous chapters illustrate with simple models the emergence of a new science of sound that accounts not only for spectral and refractive characteristics of waves but also addresses the amplitude and phase of these waves. In this chapter, these concepts are taken further and related to the development of acoustic analogues of other physical phenomena ranging from quantum phenomena to general relativity. These analogues may offer perspectives for applications and technological developments of this new science of sound. In this chapter, we first introduce the concept of phase bit (φ-bit) based on the fermion-like behavior of phonons in some elastic structures as an analogue of a quantum bit (qubit). The analogy with the notion of spin suggests the possibility of developing quantum information technologies based on superposition of elastic waves as well the capability of achieving exponentially parallel algorithms utilizing the non-separability of elastic waves. We then consider the analogy between fermion-like elastic waves (waves with spinor characteristics) supported by a structure subjected to a spatio-temporal modulation of its properties. We show the analogy between the equation that drives the dynamics of this elastic system and the Dirac equation for a charged particle including an electromagnetic field. The modulation can be used to tune the spinor part of the elastic waves suggesting that it can work as a gauge field analogue. Staying within the realm of analogies with quantum phenomena, we explore the acousto-hydrodynamics of bubbles in a fluid irradiated with an acoustic standing wave. We argue that the secondary sound field emitted by bubbles may lead to self-interaction that can modify the translational motion of bubbles. This phenomenon is reminiscent of the pilot wave model of quantum mechanics and suggests the possibility of acoustic bubbles to exhibit particle-wave duality. Finally, we review within the context of simple models the analogy between the propagation of acoustic waves in moving fluids and general relativity. We relate these concepts to the model of a one-dimensional harmonic crystal subjected to a directed spatio-temporal modulation of its stiffness. The dynamics of this system is described within the context of interpretations based on differential geometry.