Understanding Doppler Shift Equations for Calculating Object Velocity

In summary, the conversation discusses using the Doppler shift to calculate the velocity of a moving object. The equations provided are used to determine the observed frequency when the source or receiver is moving, and the use of plus or minus signs depends on the direction of movement. There is also an all-in-one equation that can be used for both a moving source and receiver, which the speaker prefers. It is possible to use this equation to calculate the velocity of the moving object if the experiment involves bouncing sound waves off of the object at a known frequency and measuring the returned frequency.
  • #1
icosahedral
2
0
So I'm planning to start a project using the Doppler shift to calculate the velocity of a moving object.

The problem is, I'm not sure which equations I should use, and I saw many different equations around the Internet.

So are these equations correct? If not, can someone tell me what the correct ones are?

Equations:

Source moving towards you: f’ observed frequency
f’ = f / [1 – (v/vs)]

Source moving away from you: f’ observed frequency
f’ = f / [1 + (v/vs)]

Thank you very much!
 
Physics news on Phys.org
  • #2
Forgive me for not knowing how to type out formulas, but here it is. This is the equation we used in my past physics course. It's kind of an all-in-one equation, and you decide how to use it based on the problem. The left side of the equation is the new frequency received taking the doppler effect into account. On the right side, the first f is the original, emitted frequency. v is the speed of sound in your particular medium, could be air or water or whatever. The the u thing in the numerator is the speed of the object that is receiving the frequency. The u in the denominator is the speed of the object emitting the frequency. There are plus-minus signs on the top and bottom, and you must decide whether to use the plus or minus sign. The saying is: "Upper approaching, lower receding." This refers to which sign you use. First look at the numerator, it considers the object receiving the frequency. Is it approaching the sound source or moving away from it? If it is approaching, use the "upper" sign, in this case the plus. If it is moving away, use the "lower" sign, in this case the minus. You do the same thing for the denominator, except you consider the source. Is the sound source approaching the receiver or moving away from it? If it's approaching, use the upper sign, which would be the minus now. If it's moving away, use the "lower" sign which would be the plus. You should notice that the two plus-minus signs are different. You MUST write it the way I did for it to work with the "upper approaching, lower receding" saying. Though if you think about it intuitively, you can figure out which sign to use without using the saying. I understand if this is more confusing than what you were trying to do or what other people might do, but it's nice because you only have to know one equation.

EDIT: In case you didn't realize, the sub-r stands for "receiver" and the sub-s stands for "source" so you remember which one is which.
 

Attachments

  • doppler.jpg
    doppler.jpg
    7.4 KB · Views: 819
Last edited:
  • #3
As for your equations, they look good. Except I don't think you could take into account a moving source AND a moving receiver at the same time. The one I just posted can do that calculation. So depending on what you are actually doing, yours might work fine. But again I prefer the one I posted because you only need to remember one equation and it works for all situations, you just need to figure out which signs to use. Let me know if I didn't explain it well enough.
 
  • #4
Thank you!

But is it possible to use this equation to calculate the velocity of the moving object?
 
  • #5
Yes, but what is your actual experiment like? Do you have some sort of sonar motion detector? As long as you can bounce sound waves off of your object at a known frequency and receive the returned sound waves and measure their frequency, you could do it.
 

1. What is the Doppler shift equation?

The Doppler shift equation is a mathematical formula that describes the change in frequency or wavelength of a wave due to the relative motion between the source of the wave and the observer.

2. How is the Doppler shift equation used in science?

The Doppler shift equation is used in various fields of science such as astronomy, meteorology, and acoustics to study the motion of objects and to calculate their velocities. It is also used in medical imaging to measure blood flow and in radar systems to detect the speed and direction of moving objects.

3. What are the variables in the Doppler shift equation?

The variables in the Doppler shift equation include the original frequency or wavelength of the wave (f0 or λ0), the observed frequency or wavelength (fobs or λobs), the velocity of the source (vs), the velocity of the observer (vo), and the speed of the wave in the medium (v).

4. How do you calculate the Doppler shift using the equation?

To calculate the Doppler shift using the equation, you first need to determine the values of all the variables. Then, you can plug these values into the equation (fobs = f0 × (v ± vo) / (v ± vs)) and solve for the observed frequency or wavelength.

5. What are some real-life applications of the Doppler shift equation?

The Doppler shift equation has many real-life applications, including measuring the speed of stars and galaxies in astronomy, studying weather patterns in meteorology, and detecting the presence of blood clots in medical ultrasound. It is also used in traffic speed cameras, speed guns, and police radar to measure the speed of moving vehicles.

Similar threads

  • Other Physics Topics
Replies
4
Views
1K
Replies
6
Views
2K
  • Other Physics Topics
Replies
14
Views
1K
  • Astronomy and Astrophysics
Replies
6
Views
892
  • Introductory Physics Homework Help
Replies
14
Views
1K
  • Other Physics Topics
Replies
12
Views
2K
Replies
3
Views
631
  • Introductory Physics Homework Help
Replies
6
Views
565
  • Special and General Relativity
Replies
17
Views
2K
Replies
1
Views
683
Back
Top