Sound is the mechanical propagation of vibrational waves from the jostle of atoms. From a physiological and psychological standpoint, sound is the sensation of such waves in an audible frequency range.

Sound emanates from an oscillation in pressure in a vicinity and propagates away as waves of vibrations through a medium with internal forces (that is, a matter consistency with some degree of elasticity). A *medium* is the matter which abets sound. Sound cannot travel through a vacuum. The particles in the transmission medium – whether gas, liquid, or solid – are not transported, but merely momentarily spatially displaced. Sound forms waves as a natural coherence.

The speed of sound depends upon the density and pressure of the medium through which sound traverses. Density (ρ, the Greek letter rho) is a measure of mass and volume: *ρ = m/V*, where *m* is mass and *V* volume. Pressure (*p*) is a scalar quantity related to a vector of force: *p = F/A*, where *F* is the magnitude of the normal force and *A* is the area of contacted surface. Normal force (*F _{n}*) is a force perpendicular to the contacted surface.

Temperature affects the speed of sound, as does the viscosity and motion of the medium. Medium viscosity determines the rate at which sound is attenuated. Viscosity is resistance to deformation.

Sound refracts when moving through a medium with inconstant physical properties.

A moving medium hastens or slows the speed of a sound wave, depending upon the coincidence of their movements. Medium and sound moving in the same direction speeds sound. If in opposite directions, the speed of sound is reduced by the speed of the medium.

A *fundamental physical constant* is a fixed, dimensionless, universal quantity. 2 such constants related to the speed of sound are the proton-to-electron mass ratio and the fine-structure constant. These constants respectively characterize the mass ratio of basic atomic constituents and the strength of their electromagnetic interaction. These constants are critical to sound because sound derives from the fundamental character of matter.

The proton-to-electron mass ratio (µ or ß) is the hypothetical rest mass of a proton divided by that of an electron (*m _{p}/m_{e}*). These measures of mass are hypothetical because protons and electrons are never at rest.

The *fine-structure constant* (*а*, the Greek letter alpha) characterizes the strength of electromagnetism: the specific quantification of electromagnetic interaction between charged particles. *а* is equivalent to *e*, the elementary electric charge, which is the coupling strength of an elementary charged particle (electron or proton) with the electromagnetic field. *а = e = ~1/137*.

The finely tuned values of *а* and µ, and the balance between them, govern nuclear reactions, including stellar nuclear synthesis, which leads to the creation of essential biochemical elements, including carbon. If the ratio of *а* and µ were not as they are, carbon could not be synthesized, and life chemically unimaginable. The *а*-µ balance also provides for the narrow “habitable zone” in space where planets form near stars and life-supporting molecular structures emerge.

The speed of sound (*v*) is *v = v _{u}/A^{1/2}*, where

*v*is the speed limit for sound and

_{u}*A*is atomic mass. The upper bound for sound –

*v*– depends on fundamental physical constants only.

_{u}*v*≈ 36,100 meters/second, where

_{u}= а(m_{e}/2m_{p})^{1/2}c*а*is the fine structure constant,

*m*is electron mass,

_{e}*m*proton mass, and

_{p}*c*the speed of light limit.

The upper bound of the speed of sound (*v _{u}*) corresponds to solid hydrogen with strong metallic bonding. But this phase of hydrogen only exists at megabar pressures: beyond the pressure limit where molecular formation occurs which permits sound to be generated.

*v*is about twice as large as

_{u}*v*in diamond, the highest speed of sound measured at ambient conditions.

Sound illustrates that the signals which form phenomena all interrelate to fundamental dimensionless constants which define the physics of existence.

References:

Ishi Nobu, “A perfect balance,” in *Unraveling Reality* (2019).

K. Trachenko *et al*, “Speed of sound from fundamental physical constants,” *Science Advances* (9 October 2020).