O n t h e T r a c k o f M o d e r n P h y s i c s 4/1 The analysis of Fourier makes it possible to...
1
O n t h e T r a c k o f M o d e r n P h y s i c s 4/1 The analysis of Fourier makes it possible to decode the components of an unspecified periodic function. An oscillation which is propagated in space (e.g. along x axis), becomes "a wave". ζ (x,t)=A sin (ωt – kx), where the period is T=2π/ω and the wavelength is λ=2π/k. The sound is a simple example of wave. The human ear is able to recognize the sound of a particular individual musical instrument in the symphony in full orchestratration. Ear makes it by that an analysis of Fourier. There is 100 years since the analysis of Fourier was done via complicated mechanical devices: masses oscillating or sphere vacuums, for the sound. Today one analyzes the sound with a simple computer and the virtual oscilloscope (http://polly.phys.msu.su/~zeld/oscill.html ) Virtual oscilloscope Harmonic analyzer of de Sir. W. Thomson Sound analyzer of König (Charles University, Prague) Harmonize glass It is not easy to obtain a simple monochromatic sound. Only one good wine glass can produce it. If wine is added, the song changes. Big cognac glass (4000 cm 3 ) f=290Hz Narrow and isolated peak is called delta of Dirac. Paul Adrien Maurice was English and owes his beautiful name to the mother, who was Suisse. Other that its "delta", it formulated a quantum equation, from which in 1930 the existence deduced from a positive electron. The positron was discovered in the cosmic rays in 1932. First he made assumptions on the formation of the solar system starting from a nebula. The existence of stable particular points between Jupiter and the Sun were confirmed from the astronomical observations only recently (1996). These small African artisanal animals make the same operation as the complicated analyzer of Sir Thomson and H. Helmholtz: they raise the vibrations, each one at its particular own frequency! Laplace’s transformation is generalized approach of Fourier: each function, not necessarily periodic can be substituted. For transformed of Laplace are delighted the electric theorists of circuits, considering which it makes it possible to solve complicated differential equations. scillating towers are in front of the Faculty of Chemistry of the University of Berlin Magic flute A simple flute produces a very complex sound, with various harmonic components, according to whether the flute remains closed or open. The its characteristic is called "stamp". Transormé de Fourier et transformé inverse Transformation of Fourier "seeks" if in the periodic function (as a vibration) are specific frequencies: the periodic function of period 2π is developed in series: The black curve has two components: sin2x and sin(3x+0.2); it is superimposed with the pink sinusoid the two periods, with the orange sinusoid the three periods. La Pierre de Rosette, British Museum J.-B.-J. Fourier (1768-1830). Napoleon made in Egypt two invaluable discoveries: the basalt plate, known as „la Rosette" and the professor of analysis of Polytechnic Ècole Jean-Baptist-Joseph Fourier. The first, containing one of the decrees of Ptolemeus V(196 D.C.) registered in hieroglyphes, demotic and Greek allowed in 1822 J.F. Champollion to decode the Egyptian writing. 1290 Hz 290 Hz 1 ) ( 0 ; ) ( 0 ; 0 ) ( t t t t t d e F t f dt e t f F t i t i ) ( 2 1 ) ( ) ( 2 1 ) ( Wine glass (125cm 3 ) f=1290 Hz nxdx x f b nxdx x f a nx b nx a a x f n n n n n sin ) ( 1 cos ) ( 1 ) sin cos ( 2 1 ) ( 1 0 During the same time Pierre- Simon de Laplace lived. Recommended by Alembert became in 1773 member of the French Academy of Science, and in 1796 professor of L’École Normale in Paris. P.-S. de Laplace (1749- 1827) 0 ) ( ) ( dt e t f s F st ib a s t f t f e f t f f t cos sin 1 ) /( ) /( ) /( 1 / 1 / 1 2 2 2 s s F s F s F s F s F + U in U out R 1 R 2 C t in out dt U RC U 0 1
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Transcript of O n t h e T r a c k o f M o d e r n P h y s i c s 4/1 The analysis of Fourier makes it possible to...
O n t h e T r a c k o f M o d e r n P h y s i c s
4/1
The analysis of Fourier makes it possible to decode the components of an unspecified periodic function.
An oscillation which is propagated in space (e.g. along x axis), becomes "a wave".
ζ (x,t)=A sin (ωt – kx), where the period is T=2π/ω and the wavelength is λ=2π/k.
The sound is a simple example of wave. The human ear is able to recognize the sound of a particular individual musical instrument in the symphony in full orchestratration. Ear makes it by that an analysis of Fourier.
There is 100 years since the analysis of Fourier was done via complicated mechanical devices: masses oscillating or sphere vacuums, for the sound. Today one analyzes the sound with a simple computer and the virtual oscilloscope (http://polly.phys.msu.su/~zeld/oscill.html)
Virtual oscilloscopeHarmonic analyzer of de Sir. W. Thomson
Sound analyzer of König (Charles University, Prague)
Harmonize glass
It is not easy to obtain a simple monochromatic sound. Only one good wine glass can produce it. If wine is added, the song changes.
Big cognac glass (4000 cm3) f=290Hz
Narrow and isolated peak is called delta of Dirac. Paul Adrien Maurice was English and owes his beautiful name to the mother, who was Suisse.Other that its "delta", it formulated a quantum equation, from which in 1930 the existence deduced from a positive electron. The positron was discovered in the cosmic rays in 1932.
First he made assumptions on the formation of the solar system starting from a nebula. The existence of stable particular points between Jupiter and the Sun were confirmed from the astronomical observations only recently (1996).
These small African artisanal animals make the same operation as the complicated analyzer of Sir Thomson and H. Helmholtz: they raise the vibrations, each one at its particular own frequency!
Laplace’s transformation is generalized approach of Fourier: each function, not necessarily periodic can be substituted. For transformed of Laplace are delighted the electric theorists of circuits, considering which it makes it possible to solve complicated differential equations.
The oscillating towers are in front of the Faculty of Chemistry of the University of Berlin
Magic flute
A simple flute produces a very complex sound, with various harmonic components, according to whether the flute remains closed or open. The its characteristic is called "stamp".
Transormé de Fourier et transformé inverse
Transformation of Fourier "seeks" if in the periodic function (as a vibration) are specific frequencies: the periodic function of period 2π is developed in series:
The black curve has two components: sin2x and sin(3x+0.2); it is superimposed with the pink sinusoid the two periods, with the orange sinusoid the three periods.
La Pierre de Rosette, British Museum
J.-B.-J. Fourier (1768-1830).
Napoleon made in Egypt two invaluable discoveries: the basalt plate, known as „la Rosette" and the professor of analysis of Polytechnic Ècole Jean-Baptist-Joseph Fourier.
The first, containing one of the decrees of Ptolemeus V(196 D.C.) registered in hieroglyphes, demotic and Greek allowed in 1822 J.F. Champollion to decode the Egyptian writing.
1290 Hz
290 Hz
1)(
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t
tt
tt
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dtetfF
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)(2
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Wine glass(125cm3) f=1290 Hz
nxdxxfb
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nxbnxaaxf
n
n
nnn
sin)(1
cos)(1
)sincos(2
1)(
10
During the same time Pierre-Simon de Laplace lived. Recommended by Alembert became in 1773 member of the French Academy of Science, and in 1796 professor of L’École Normale in Paris.
P.-S. de Laplace (1749-1827)
0
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tf
tf
ef
tf
f
t
cos
sin
1
)/(
)/(
)/(1
/1
/1
2
2
2
ssF
sF
sF
sF
sF
+
Uin
Uout
R1
R2
C
t
inout dtURC
U0
1
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