Energy of twin source interference

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Homework Help Overview

The discussion revolves around the energy of twin source interference, particularly focusing on the intensity of waves and their dependence on amplitude. Participants are examining the mathematical relationships involved in wave interference and the implications of various terms in the equations presented.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to identify which terms in the equations represent amplitude and how these relate to intensity. There are questions regarding the time dependence of certain terms and how to derive relationships from the given equations.

Discussion Status

Some participants have offered insights into the relationship between amplitude and intensity, suggesting that squaring amplitude relates to intensity. There is ongoing exploration of the implications of distance on path difference and the wavenumber in the context of wave interference.

Contextual Notes

Participants are working with specific equations and terms, such as the wavenumber and path difference, while also referencing external resources for their workings. There is a focus on understanding the transformations needed to connect different parts of the problem.

elemis
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Homework Statement



http://www.mediafire.com/view/?3efd7326e49kteb

I've worked out all except part (iv).

These are my workings : http://www.mediafire.com/view/?elswc5g5412zhzq

I just can't see how to get rid of cos(pi*(x1+x2/λ -wt).

Also, where does the I0 come from ?
 
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Intensity of a wave, at a point, depends on its amplitude at that point. Which terms of the equation in (ii) represents amplitude at P?
 
I'm guessing A and the second cosine term ? This is just an educated guess, I can really see how or why. Is it to do with the envelope and the carrier wave which are represented by the two cosine terms individually ?
 
did that part is time dependent?
 
mukundpa said:
did that part is time dependent?

What ?
 
The first two terms are not changing with time thus they give the amplitude, the third part is time dependent and thus whole equation gives wave displacement at any time t.
 
mukundpa said:
The first two terms are not changing with time thus they give the amplitude, the third part is time dependent and thus whole equation gives wave displacement at any time t.

Okay so taking 2A*first cosine term and squaring it should give me some proportional to Intensity since I = kA^2

Is Io = A^2 then ?
 
What is k in the equation and if the distance of P is large what is the path difference in terms of θ ?
 
mukundpa said:
What is k in the equation and if the distance of P is large what is the path difference in terms of θ ?

If P is very very far away then the path difference is dsinθ and k is the wavenumber i.e. 2pi/λ
 
  • #10
Thus the amplitude at P is 2A cos (π d sin θ / λ)
 
  • #11
mukundpa said:
Thus the amplitude at P is 2A cos (π d sin θ / λ)

I've worked that out already in the workings I attached in the OP.

How do I take this and transform into the equation in part (iv) ?
 
  • #12
I at P is square of this and A2 = I0
 

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