Confusion in Doppler shift equation?

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Discussion Overview

The discussion centers around the derivation of the Doppler shift equation for a moving observer and a stationary source, specifically focusing on a particular algebraic step in the process. Participants are seeking clarification on the mathematical reasoning behind the equation.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant is attempting to build the Doppler shift equation and is confused about the origin of the term (1 - v/u)-1.
  • Another participant references a previous equation involving Δt0 and Δts, suggesting that the confusion can be resolved through algebraic manipulation.
  • There is a request for clarification on whether Δt0 should be treated as 1 in the context of the algebra being discussed.
  • Participants express a desire to understand the algebraic steps involved rather than just the final result.

Areas of Agreement / Disagreement

The discussion remains unresolved, with participants expressing confusion and seeking clarification on specific algebraic steps without reaching a consensus on the interpretation of Δt0.

Contextual Notes

There are missing assumptions regarding the definitions of variables and the context of the equations being referenced, which may affect the understanding of the algebra involved.

Tim541541
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I'm just trying to build Doppler shift equation for Moving observer and stationary source. I have an problem in a step. I'm attaching a screen-shot please check it and tell me where to this step ( 1 - v/u)^-1 comes from ?

Thanks in advance.
 

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  • 2016-01-02_202639.png
    2016-01-02_202639.png
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The previous line is ##\Delta{t}_0=\Delta{t}_s+\frac{v\Delta{t}_0}{u}##. It's just algebra from there.
 
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Solve for Δt0 in the first equation at the attached image.
 
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Nugatory said:
The previous line is ##\Delta{t}_0=\Delta{t}_s+\frac{v\Delta{t}_0}{u}##. It's just algebra from there.
Thank you Nugatory for reply. Can you tell me is that delta t sub o will be mentioned as 1 here ? Actually i just really want to understand algebra behind it.
 
Tim541541 said:
Thank you Nugatory for reply. Can you tell me is that delta t sub o will be mentioned as 1 here ? Actually i just really want to understand algebra behind it.
I'm sorry, but I don't understand what you mean by "will be mentioned as 1 here"... The algebra is, as Erland says above, just solving for ##\Delta{t}_0##.
 

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