Doppler Shift: Deriving a Formula for Both Moving Objects

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Discussion Overview

The discussion revolves around deriving a formula for the Doppler shift when both the source and the observer are in motion. Participants explore the implications of moving objects on the observed frequency of waves, particularly in the context of sound waves in a medium.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant notes the existence of separate formulas for when either the source or the observer is moving, and questions how to derive a formula for both moving simultaneously.
  • Another participant provides a general formula for the Doppler effect, indicating the need to use appropriate signs based on the direction of motion of the source and observer.
  • Clarifications are sought regarding the definitions of frequencies f and f', as well as the relative velocities v_d and v_s in relation to the medium.
  • Further confirmation is provided on the use of signs in the formula depending on whether the source and observer are moving apart or towards each other.

Areas of Agreement / Disagreement

Participants generally agree on the structure of the Doppler effect formula and the definitions of the variables involved. However, there is ongoing clarification regarding the application of signs in the formula, indicating some uncertainty in the details of the derivation.

Contextual Notes

Participants express uncertainty about the correct application of signs in the Doppler effect formula, which may depend on specific scenarios of motion. There is also a reliance on the definition of velocities relative to the medium, which may not be universally applicable.

Who May Find This Useful

This discussion may be useful for students or individuals interested in understanding the Doppler effect, particularly in scenarios involving multiple moving objects and the mathematical derivation of related formulas.

StephenPrivitera
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My book derives two formulas for Doppler shift. One for when the source moves and one for when the observer moves.
What about when both are moving?
I tried deriving it myself... but I couldn't :(
If you want, you could just give me a hint on how to derive it.
 
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The general formula for the doppler effect should be:

[tex]f'=f_o(\frac{v \pm v_d}{v \pm v_s})[/tex]

In this, [tex]v[/tex] should be the velocity the wave is traveling at (like 343 m/s for sound in air). So if you have both the detector and source moving, just make sure you use the correct sign in front of each and you should be set. Does this help?

-Jason
 
Yes that helps a lot. Do you use - on the botton when they are moving apart and + on the top when they are moving apart?
Also, can you clearly define f and f'?
f is the frequency as observed by the source?
f' is the frequency as observed by the detector?
Also, these speed v_d and v_s are relative to the medium in which the wave travels correct?
 
Last edited:
Let me try and answer these one at a time:

If they are moving away from each other, than yes you would use + on top, and - on bottom I believe.

You have the f's correct as well. [tex]f'[/tex] will be your new frequency (as observed by the detector), and [tex]f_o[/tex] will be the initial frequency (as sent out by the source.

As for the velocities, once again you are correct. They are relative to the medium.

-Jason
 

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