Doppler Shift: Deriving a Formula for Both Moving Objects

In summary, the conversation discusses the concept of the Doppler effect and its two formulas for when the source and observer are moving. It is noted that when both are moving, the general formula is f'=f_o(\frac{v \pm v_d}{v \pm v_s}), with the correct sign used depending on the direction of movement. The frequencies f and f' are defined as the observed frequency from the source and detector, respectively, and the velocities v_d and v_s are relative to the medium.
  • #1
StephenPrivitera
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0
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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  • #2
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
 
  • #3
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?
 
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  • #4
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
 

What is Doppler shift?

Doppler shift is the change in frequency or wavelength of a wave that occurs when the source of the wave is moving relative to the observer.

How is the Doppler shift formula derived?

The Doppler shift formula is derived by considering the change in distance between the source and the observer as the source moves, and using the fact that the frequency of a wave is inversely proportional to its wavelength.

Can the Doppler shift formula be used for both moving objects?

Yes, the Doppler shift formula can be used for both moving objects, as long as the relative motion between the source and the observer is known.

What factors affect the magnitude of Doppler shift?

The magnitude of Doppler shift is affected by the velocity of the source or observer, the speed of the wave, and the angle between the direction of motion and the line connecting the source and the observer.

What are some practical applications of Doppler shift?

Doppler shift has many practical applications, including in radar and sonar systems, medical imaging, and astronomy. It can also be used to measure the speed of objects, such as cars or stars, and to study the motion of galaxies and the expansion of the universe.

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