Sound Wave as a Particular Case of the Gravitational Wave

Abstract

It is demonstrated that the universally accepted system of gas-dynamic (hydrodynamic) equations is applicable only to homogeneous (isentropic) media and requires advancement to get applicable to non-homogeneous media. A generalized equation of gravitational wave for adiabatic and ideal media is obtained from advanced system. From this equation, in turn, is obtained an equation of acoustic wave, which is plane and different form the known equation in that the phase speed of the wave in the Earth atmosphere obviously depends on altitude, <i>i.e. C = C (z, T)</i> instead of accepted <i>C = C (T)</i>. Thus, acoustic wave is a short-period gravitational wave in which gravitational effects are revealed at altitudes <i>z</i> > 2.3 × 10<sup>3</sup> m, which leads to amplification of refraction of sound. The sphere of applicability of the equation is determined and it is demonstrated that it is true only up to the upper boundary of the troposphere ( <i>z</i> ≤ 11 - 12km.) above which anomalous processes develop in the atmosphere

Peculiarities of Sound Wave in Moving Medium

“…Therefore, these waves have nothing in common with the waves generated as a result of perturbation of gravitational field and can be propagated in vacuum. The equation for linear gravity wave in immovable inhomogeneous medium was first obtained in the paper [9] where it was shown that exactly this equation describes propagation of sound in the Earth atmosphere correctly. Thus, the generally received opinion that the gravitational field does not have any impact on the sound wave was invalidated.…”

“…In this section we will obtain analogous equation for moving inhomogeneous medium. Let's consider the generalized system of hydrodynamic equations for inhomogeneous medium in gravitational field of the Earth [9] ( ) ( )…”

“…However it is still considered universal and up to now has been applied to inhomogeneous medium like the Earth atmosphere [1]- [5] or the ocean [5]- [8]. In recent works [9] [10] it was demonstrated that allowing for the effect of the gravitational field of the Earth this equation needs to be perfected. It resulted in improvement of great number of known gas or hydrodynamic relations as well as to new understanding of the most important properties of medium like compressibility and incompressibility.…”

Correct Definition of Sound Speed and Its Consequences in the Tasks of Hydrodynamics

“…from which the equation for any wave in Earth's gravitational field, including sound wave equation, can be obtained [4]. We will seek for all perturbed quantities in the form ( , , ) = ( ) exp[ ( − )] and take into account that…”

“…It appeared that the equation in its current form is fair only for homogeneous medium and as any medium in gravity field is more or less inhomogeneous, it needs to be generalized. The generalized mass conservation equation is obtained in work [4], in the right part of which an additional summand is entered determining the change of density of constant mass, under isobaric change of its volume as a result of temperature variations conditioned by entropy oscillations in inhomogeneous (nonisentropic) medium. When the first summand equals zero, which is the condition for incompressibility of the medium, the second summand remains, equaling isobaric change of its density.…”