Symmetry Properties of Acoustic Fields

Abstract

WS Gan introduced symmetry properties of the acoustic field in 2007. This has been confirmed by the successful fabrication of the acoustical metamaterials, diverse applications of time reversal acoustics and that phonon is a Goldstone mode. The form invariance of the linear acoustic field equation demonstrates the symmetry properties of acoustic fields. Likewise, form invariance is also applicable to nonlinear acoustic field equations such as Burgers equation, Westervelt equation and Shapiro–Thurstone equation. The symmetry between the acoustic velocity field and stress field is a further demonstration of the symmetry properties of acoustic fields. Symmetry is the theoretical framework of acoustical metamaterials. The propagation of sound waves in fluids obeys both translational and rotational symmetry, whereas propagation of sound waves in solids obeys rotational symmetry but broken translational symmetry due to the discrete and periodic nature of the crystal gives rise to phonons. The scale invariance or symmetry property of the turbulence field also supports the symmetry properties of acoustic fields as turbulence field is intrinsically acoustic field considering that turbulence is the source of the aerodynamic noise.