Acoustics of noise, vibration, and harshness

Abstract

In this paper, we will go to a more fundamental level of treating acoustics. We introduced the gauge invariance into the acoustic wave equation of motion in 2007. This is an important milestone in the history of gauge invariance. The earliest gauge invariance is shown by Maxwell’s electromagnetic wave equations. The root of acoustics originated from fluid mechanics. We show that the usual form of acoustic wave equation for fluids is in fact the linearized form of the Navier Stokes equations. Hence there is in fact, no need to use acoustic analogy to derive the formula for the jet noise which was done by James Lighthill. In this paper we also treat finite amplitude sound wave and finite amplitude vibration using the deductive approach. This is a generalization of the linear theory to the nonlinear theory using relativistic and curvilinear spacetime treatment. This produces the linear case as a special case of the nonlinear case. The usual method is the reverse which starts from the linear theory and extend to the nonlinear theory. This will miss out some useful information. The treatment of vibration will need to incorporate the theory of elasticity. This paper is also the first introduction of singularities into vibration. Singularities is mathematically more sophisticated than resonance.