Gauge-theoretic Study of Kundt Tube Experiment and Spontaneous Symmetry Transitions

Abstract

In the Kundt's experiment of acoustic resonance in closed tubes, two characteristic lengths were observed: one is the wave-length of the sound waves in resonance and the other the scale of dust striation. The latter has remained unresolved for its formation mechanism. Based on the Fluid Gauge Theory proposed recently by the author, formation mechanism of the dust striation is studied. When the sound is weak enough, the striation is unobserved. Once the wave intensity exceeds a threshold value, dust striations are formed. Formation of the dust striation is understood as a spontaneous transition of symmetry in the acoustics. According to the Theory, there is a transition of stress field within the fluid flow. Whereas the stress field is isotropic before transition, it becomes anisotropic after the transition. This is analogous to the spontaneous symmetry breaking known in the field theory. Lagrangian structures of both systems are verified to be analogous either.