I. Sound-wave energy density in a gaseous ether.---[Return home]

We consider a plane sound-wave in the gazeous ether for which the displacement equation is: . Ao is the amplitude, f the frequency and c the sound-wave velocity (=light speed in the ether).

This equation means (figure below) that a layer of ether oscillates with the amplitude Ao at the frequency f relatively to any chosen X0 position.

As the ether is considered as to obey the newtonian mechanics, the kinetic energy of the volume dV of ether is: where is the volumic mass of the ether.

As in Xo the velocity V is the derivative of the displacement x(t) : , the energy density (energy by cubic meter) in x(t) is:

But to calculate the whole energy of an extended wave, it is more easy to use the average of this variable energy density than to use always this formula (a bit too complicated).

To obtain an usable average, we have to calculate the mean along a wavelength of the wave (with a fixed time) or along a period at a given fixed position.

The time or the position chosen is without influence on the result and, as we have for the cosinus fonction:

Time average (Xo fixed) :

Space average (To fixed):

The integration is made with a change of variable and by partial integration leading to the formula:

With this result the averaged energy density is: , and the whole newtonian kinetic energy contained in a volume V of a constant sound-wave in amplitude and in frequency is: E= Da.V. This energy is the energy needed to produce the sound-wave, or the sound-wave energy.

Finally, I have to say, that when the frequency is very high or when the amplitude is important the density or the sound-wave velocity may be modified and thus this calculation is only an approximation. But if the reader take knowledge up to the gravity theory of what is said here, he will understand that this change of velocity and of energy density is responsible of gravity (force).

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