Control of the Gravitational Energy by means of Sonic Waves

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Control of the Gravitational Energy by means of Sonic Waves

Fran de Aquino

To cite this version:

Fran de Aquino. Control of the Gravitational Energy by means of Sonic Waves. 2015. �hal-01230149v2�

Fran De Aquino

Professor Emeritus of Physics, Maranhao State University, UEMA.

Titular Researcher (R) of National Institute for Space Research, INPE Copyright © 2015 by Fran De Aquino. All Rights Reserved.

It is shown here that the incidence of sonic waves on a solid can reduce its gravitational mass. This effect is more relevant in the case of the Aerogels, in which it is possible strongly reduce their gravitational masses by using sonic waves of low frequency.

Key words: Gravitational Energy Control, Gravitational Mass, Sonic Waves, Sound Pressure.

The quantization of gravity showed that the gravitational mass mg and the inertial mass m_i are correlated by means of the following factor [1]:

( )

1 1

1 2 1

2

0

0 ⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟ −

⎠

⎜⎜ ⎞

⎝ +⎛ Δ

−

=

= m c

p m

m

i i

χ g

where is the rest inertial mass of the particle and is the variation in the particle’s kinetic momentum; is the speed of light.

0

mi

Δp

c

When an electromagnetic wave strikes an atom, it interacts electromagnetically with the atom, acting simultaneously on all its structure. Unlike a sonic wave that strikes the internal particles of the atom isolatedly, interacting mechanically with them. Thus, if a lamina of monoatomic material, with thickness equal toξ contains atoms/mn ³, then the number of atoms per area unit isnξ. Thus, if the sonic wave with frequency incides perpendicularly on an area of the lamina it reaches

f ξ S

nS atoms. Consequently, the wave strikes on ZnSξ orbital electrons^* (Zis the atomic number of the atoms).

Therefore, if it incides on the total area of the lamina, , then the total number of electrons reached by the radiation is

Sf fξ ZnS N = .

* Assuming that, all of them are reached by the sonic wave.

The number of atoms per unit of volume, , is given by n

( )

2

0

A n N ρ

=

where is the

Avogadro’s number;

kmole atoms

N₀ =6.02×10²⁶ /

ρ is the matter density of the lamina (in kg/m³) and A is the molar mass(kg/kmole).

When the sonic wave incides on the lamina, it incides N_f front electrons, where

( )

f e

f ZnS

N ≅ φ , φ_e is the “diameter” of the electron inside an atom^†, which is

[

e m

10 13

4 . 1 × ⁻

φ = 2]. Thus, the sonic wave incides effectively on an area S=N_fS_e , where

2 4 1

e

Se = πφ is the cross section area of one atom.

After these collisions, it carries out with the other orbital electrons (See Fig.1).

collisions

n

Fig. 1 – Collisions inside the lamina.

electron Se

Wave

Thus, the total number of collisions in the volumeSξ is

† The diameter of the electron and protons depends on the region where it is placed.

2

( )

( )

³

ξ φ ξ φ

S n

S n S n S n n

N N

l

e e l e l collisions f

collisions

= + = + − =

=

The power density, , of the sonic radiation on the lamina can be expressed by

D

( )

4

e fS N

P S

D = P =

We can express the total mean number of collisions in each orbital electron, , by means of the following equation

n1

( )

⁵

1 N

N n = n^{total phonons collisions}

Since in each collision a momentum h λ ^‡ is transferred to the atom, then the total momentum transferred to the lamina will be

(

n N

)

h λ p= ₁

Δ . Therefore, in accordance

with Eq. (1), we can write that

( )

( )

( )

( )

⁶

1 1

2 1

1 1

2 1

2

0 2

0 1 0

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎥ −

⎦

⎢ ⎤

⎣ +⎡

−

=

⎪⎭=

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎥ −

⎦

⎢ ⎤

⎣ +⎡

−

=

λ λ

c m N h

n

c m N h m n

m

i collisions phonons total

i l

i l g

Since Eq. (3) gives N_collisions =n_lSξ , we get

( ) (

⁷

2 n Sξ

hf N P

n_{total phonons collisions} ⎟⎟⎠ _l

⎜⎜ ⎞

⎝

=⎛

)

Substitution of Eq. (7) into Eq. (6) yields

( )

( ) 1 2 1

( )

1

( )

8

2

0 2

0 ⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

⎥⎥

⎥

⎦

⎤

⎢⎢

⎢

⎣

⎡

⎥ −

⎥⎦

⎤

⎢⎢

⎣

⎡

⎟⎟⎠

⎜⎜ ⎞

⎝ + ⎛

−

= ξ λ

c m S h hf n

P m

m

i l l

i l g

‡ Phonon is a quantum of vibrational energy. The phonon energy is given by ε =_hω =hf , and its velocity is v=λf (λis the wavelength). Thus, the momentum carried out by a phonon is

λ λ

ε v hf f h

p= = = . Thus, the expression of

the momentum carried out by the phonon is similar to the expression for the momentum carried out by the photon [3].

Substitution of Pgiven by Eq. (4) into Eq. (8) gives

( )

( ) ( ) 1 1

( )

9

1 2 1

2

0 2

0 ⎪

⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

⎥⎥

⎥

⎦

⎤

⎢⎢

⎢

⎣

⎡

⎥ −

⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟⎠

⎜⎜ ⎞

⎝ + ⎛

−

= λ

ξ c m

S n f

D S N m

m

l i e l f l

i l g

Substitution ofNf ≅Z

( )

nlSfφe and into Eq. (9) results

e fS N S=

( )

( ) ( )

( )

10 1 1

1 2 1

2

2 0

2 2 2 3 2

0 ⎪

⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

⎥⎥

⎥

⎦

⎤

⎢⎢

⎢

⎣

⎡

⎥ −

⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝ + ⎛

−

= λ

ξ φ cf m

D S S n Z m

m

l i

e e f l l

i l g

where m_{i0( )l} =ρ_{( ) ( )l}V_l .

The speed of the sound,v, as a function of frequency, f , and wavelength,λ, is given by v=λf , (phase velocity) [4]. When the sonic wave propagates itself through the lamina its velocity is modified and becomes

( )^{l r}( )^l

r f n

n v

v_mod = =λ , where is the

sonic refractive index of the lamina, which can be expressed by the following equation:

( )^l

nr

( )^{l air la a}

r v v

n = _min . Since v_mod =λ_modf , where λmod is the modified wavelength, then we can write that

( ) ( )

( )

¹¹

mod

l r l

r n

f v

n =

= λ

λ

Substitution of λ by λ_mod into Eq. (10) yields

( )

( ) ( )

( ) ¹

( )

¹²

1 2 1

2

2 0

2 2 2 3 2

0 ⎪

⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

⎥⎥

⎥

⎦

⎤

⎢⎢

⎢

⎣

⎡

⎥ −

⎥⎦

⎤

⎢⎢

⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝ + ⎛

−

= v

f n cf m

D S S n Z m

m _rl

l i

e e f l l

i l

g φξ

Considering thatm_{i0( )l} = ρ_{( )l} S_αξ , we obtain

( ) ( )

( )

( ) 1

( )

13

1 2

1 _{2 2 2 2 2}

2 4 4 4 6 2 2

0 ⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡ + −

−

=

= S c f v

D S S n n Z m

m

l

e e f l l r l

i l g

ρ α

χ φ

ForS_f =S_α we obtain

( ) ( )

( )

( ) ¹

( )

¹⁴

1 2

1 _{2 2 2 2}

2 4 4 2 6 2 2

0 ⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡ + −

−

=

= c f v

D S S n n Z m

m

l e e l l r l

i l g

ρ

χ ^α φ

Since

( )

¹⁵

2

2

v D P

= ρ

where P is the pressure of the sonic radiation [5], then substitution of Eq. (15) into Eq. (14) gives

( ) ( )

( )

( ) ¹

( )

¹⁶

1 4 2

1 _{4 2 2 4}

4 4 4 2 6 2 2

0 ⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡ + −

−

=

= c f v

P S S n n Z m

m

l e e l l r l

i l g

ρ

χ ^α φ

This equation, deduced for phonons, is only valid for solids^§, unlike the correspondent equation deduced for photons, which is valid for solid, liquid and gases.

The speed of the sound for pressure waves in solid materials is given by

( )

17 ρ

v_solid = Y

where Yis the Young’s modulus.

Aerogels are solids with high porosity (<100 nm), with ultra low density (~3 Kg/m3 or less) and with ultra low sound speed (~110m/s) [6,7,8]. We can take Eq. (16) for a hypothetic aerogel with the following characteristics: Debye speed of soundv=110m.s⁻¹;

( ) =v v=343110=3.1

n_{rl air} ;ρ_{( )l} =3kg.m⁻³;

( ) N0 A 1 10²⁹atoms /m³

n_lsolid = ρ_{solid solid} ≅ ×

(ρ_solid is neither the bulk density nor the

skeletal density it is the specific mass of the part solid) ;S_e =πφ_e² 4=1.6×10⁻²⁶m²;

; . By substitution of these values into Eq. (16), we get

e m

1013

4 . 1 × ⁻

φ = Z≅10

( )

( ) ^{1 2 1 6 106 2}₂^{4 1}

( )

¹⁸

0 ⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡ + × −

−

=

= ⁻

f P S m

m

l i

l

g α

χ

Note that for , and

, (Loudest human voice at 1 inch reach ; Jet engine at 1 m

reach [

1m2

S_α ≅ f =20Hz / 2

120N m P=

/ 2

110N m / 2

632N m 9].), the Eq. (18) tells us that

( )

( ) 1

( )

19

0

−

≅

l i

l g

m m

§ Since a phonon is a mechanical excitation that propagates itself through the crystalline network of a solid.

This shows that under these conditions, the weight of the lamina

(

^mg_{( )}l ^g

)

will have its

direction inverted. For ;

and

/ 2

600N m P=

1m2

S_α ≅ f =20Hz the result is

( )

( ) ^85.2

( )

²⁰

0

−

≅

l i

l g

m m

In this case, the weight of the lamina besides to be inverted, it is intensified 85.2 times.

Thus, by controlling the magnitude of the gravitational mass is then possible to control the gravitational energy, gravity, etc.

Vulcanized Rubber can be as

advantageous as Aerogels. In this case we have: v=54m.s⁻¹; ρ_{( )l} ≅930kg.m⁻³;

( ) =v v=34354=6.3

n_{rl air} . The main

constituent of Vulcanized Rubber is synthetic cis- polyisoprene. Based on its chemical structure, we can calculate the value of n_l. The result is

3

29 /

10

4 atoms m n_l ≅ ×

AssumingZ = Z_{( )C} ≅ 6 and considering that

2 26

2 4 1.6 10 m

S_e =πφ_e = × ⁻ ; ,

then by substitution of these values into Eq. (16), we get

e m

1013

4 . 1 × ⁻ φ =

( )

( ) ^{1 2 1 6.4 1011 2}₂^{4 1}

( )

²¹

0 ⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡ + × −

−

=

= ⁻

f P S m

m

l i

l

g α

χ

For P=600N/m² ; S_α ≅1m² and f =0.2Hz (Infrasound^**) the result is

( )

( ) 25.8

( )

22

0

−

≅

l i

l g

m m

**Such sound waves cover sounds beneath 20 Hz down to 0.001 Hz.

4

References

[1] De Aquino, F. (2010) Mathematical Foundations of the Relativistic Theory of Quantum Gravity, Pacific Journal of Science and Technology, 11 (1), pp. 173-232.

[2] De Aquino, F. (2012) Superconducting State generated by Cooper Pairs bound by Intensified Gravitational Interaction, Appendix A. Available at: http://vixra.org/abs/1207.0008

[3] Riessland, J. A. (1973). The Physics of Phonons, Wiley-Interscience Publication.

[4] Ference Jr, M., et al., (1956) Analytical

Experimental Physics, The University of Chicago Press. Portuguese version, Ed. Edgard Blucher, S.

Paulo, Brazil, p.5.

[5] Ference Jr, M., et al., (1956) Analytical

Experimental Physics, The University of Chicago Press. Portuguese version, Ed. Edgard Blucher, S.

Paulo, Brazil, p.38.

[6] Thapliyal, P. C and Singh, K. (2014) Aerogels as Promising Thermal Insulating Materials: An Overview. Journal of Materials, Volume 2014, Article ID 127049.

[7] Gurav, J.L. et al., (2010) J. Nanomaterials, 409310.

[8] Jing, X., et al., (2013) Thermal conductivity of a ZnO nanowire/silica aerogel nanocomposite.

Applied Physics Letters, 102, 193101.

[9] https://en.wikipedia.org/wiki/Sound_pressure