Understanding Doppler Shift Equations for Calculating Object Velocity

[icosahedral]

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!

 

[Stengah]

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.

 

[Stengah]

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.

 

[icosahedral]

Thank you!

But is it possible to use this equation to calculate the velocity of the moving object?

 

[Stengah]

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.