The wave vector and wavelength conversion between electromagnetic wave

[xiaojun]

[imatfaal]

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Moderator Note

 

moved to speculations.

 

and in future please ask a question, or raise a point for debate rather than cut and paste.

 

[swansont]

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Moderator Note

And post it in speculations. This is not mainstream science.

[xiaojun]

Here on the Doppler wavelength is obtained two results，One (8) type，Another (14)，Whether it is a right.？

[swansont]

You lose me at equation (3), when you have [math]k\lambda = k\lambda(ch^2 \theta - sh^2\theta)[/math] No explanation of these additional terms.

 

And then equations 4 and 5 pop up from nowhere.

[xiaojun]

You lose me at equation (3), when you have [math]k\lambda = k\lambda(ch^2 \theta - sh^2\theta)[/math] No explanation of these additional terms.

 

And then equations 4 and 5 pop up from nowhere.

Only the expression of wave vector and the wavelength of the meeting (4) (5) of two type, the wave vector and the wavelength of the expressions can satisfy (3).

[swansont]

Only the expression of wave vector and the wavelength of the meeting (4) (5) of two type, the wave vector and the wavelength of the expressions can satisfy (3).

 

That means nothing to me. What are c, h, s and theta?

[xiaojun]

 

That means nothing to me. What are c, h, s and theta?

Theta is the parameter here, size and source motion state it on

[swansont]

Theta is the parameter here, size and source motion state it on

 

Meaning what? You need to define these terms.

[xiaojun]

 

Meaning what? You need to define these terms.

chθ=coshθ，shθ=sinhθ

[swansont]

Now explain why they suddenly appear in the equations.

[xiaojun]

Now explain why they suddenly appear in the equations.

Because the required k'λ'=kλ, and (coshθ)^2 - (sinhθ)^2=1

[swansont]

Because the required k'λ'=kλ, and (coshθ)^2 - (sinhθ)^2=1

 

What is the basis for requiring (coshθ)^2 - (sinhθ)^2=1 ? Where does the equation come from? θ just appears in your equation without prior mention or definition.

[xiaojun]

 

What is the basis for requiring (coshθ)^2 - (sinhθ)^2=1 ? Where does the equation come from? θ just appears in your equation without prior mention or definition.

No matter what value of θ have(coshθ)^2 - (sinhθ)^2=1, the θ value is determined by (7)

[swansont]

I had not gotten that far. Usually you put equations in order that they are used, i.e. something defined in equation 7 should not be used in equation 3. Also, column formatting means you read top-to-bottom of the left column.

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Ignoring, for the moment, the source of these equations, what you have done here is math. If you have found an inconsistency, then it means there is a math error.

[xiaojun]

I had not gotten that far. Usually you put equations in order that they are used, i.e. something defined in equation 7 should not be used in equation 3. Also, column formatting means you read top-to-bottom of the left column.

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Ignoring, for the moment, the source of these equations, what you have done here is math. If you have found an inconsistency, then it means there is a math error.

k'λ'=kλ= kλ[ (coshθ)^2 - (sinhθ)^2]=kλ[ (coshθ) + (sinhθ)][ (coshθ) - (sinhθ)]=k[ (coshθ) + (sinhθ)]λ[ (coshθ) - (sinhθ)]

[swansont]

Somewhere before equation 14, where you notice an inconsistency, you have made a math error of some sort. Algebra or an invalid constraint are two likely candidates.

[xiaojun]

Somewhere before equation 14, where you notice an inconsistency, you have made a math error of some sort. Algebra or an invalid constraint are two likely candidates.

Equation (14) in the wavelength and frequency of two expressions that wrong?

The following Cherenkov radiation can only be confirmed (8) holds, does not prove that (6) holds

 

[swansont]

I'm not really interested in finding your error. What I do know is that all you have done here is math, so if there is a problem, it is a math manipulation problem.

[xiaojun]

I'm not really interested in finding your error. What I do know is that all you have done here is math, so if there is a problem, it is a math manipulation problem.

All the conclusions I are derived by mathematics, a theoretical and experimental foundation strong, eager to the moderator to find the existing problems in the mathematical derivation.