The Theoretical Explanation for the Sound Barrier and its Relation to Light Refraction

Abstract

It is pointed out that application of the Doppler effect to sound waves created by airplanes leads to the conclusion that when they are accelerated to the speed of sound (Mach 1), the wavelength decreases to zero (λ=0). The de Broglie relation between momentum and wavelength (p=h/λ) which was used to predict electron diffraction therefore indicates that the momentum p of the carrier molecules of the waves must become unbounded (p=mv=∞) at that point. It is argued that it is this singularity which is responsible for the phenomenon of sonic booms. The frequency of the waves is not affected by the motion of the airplane, however, consistent with an argument used by Einstein in his prediction of the gravitational red shift. A close relationship between this interpretation for the behavior of sound waves and the corresponding theory of light refraction is noted. It is shown that in both cases Einstein’s mass-equivalence relation E=mc2 is violated.