Speed of Sound in Atmosphere of the Earth

Abstract

It is demonstrated that contemporary conception on adiabaticity of sound in the Earth atmosphere is fair in sufficient approximation only for altitudes <i>z</i> ≤ 10<sup>3 </sup>m. At higher altitudes adiabaticity of sound is violated and essential dependence of its speed on altitude is revealed which is related to heterogeneity of the atmosphere in gravitation field of the Earth. It became possible to reveal the factor of gravity field due to the fact that in the equation of the state of atmosphere considered to be ideal gas, the entropy s is taken into consideration and is written down as <i>ρ = (p, s)</i> instead of generally accepted <i>ρ = ρ(p)</i> which is fair only for isentropic media and is not applicable to the Earth. Such approach enabled to determine that apart from adiabatic mechanism of generation of sound wave there exists isobaric one and exactly this mechanism leads to dependence of sound speed on altitude which is the same as dependence on density

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

“…For homogeneous (isentropic) medium ( ⃗ ∇) = 0 and from (6) it is seen that change of density of liquid particle is indeed determined by (2). For inhomogeneous medium we can write…”

“…Thus, complete change of density consists of two parts, first of which is determined by (2). The second part describes change of density of substance of constant mass as a consequence of isobaric change of volume which can occur only at the cost of change of temperature, which in turn, in absence of heat source, is possible only in case of change of entropy; that is,…”

“…Therefore, for water, as well as for air at sea level, the second term in (9) can be neglected [2]. Let us present all the variables in the form of the sum of fixed and perturbed values as follows:…”

“…Discussion of this problem with particular intensity started from 2012, after publication of work [2]. The subsequent papers based on the critical analysis of the works of other authors persuasively proved existence of the aforementioned contradictions, suggesting the ways of overcoming them.…”

“…Irrelevance of condition of incompressibility to liquids was shown in work [1]. Upon correct determination of sound speed [2], according to which its true (real) value in the medium is determined by combination of adiabatic ( ) and isobaric ( ) sound speeds, it became evident that compressibility and incompressibility have thermodynamic rather than mechanic meaning and they are directly related to homogeneity or inhomogeneity of the medium [3]. Homogeneous medium, which is free from the influence of external force field, is always compressible and sound speed in it is adiabatic.…”