Doppler effect equation....which one is right?

[Sarahgelatinano]

I have two conflicting equations used to solve the doppler effect. Which one is correct, or can you use both of them?

1) f=f' ( 1+ (Vo/V) ) / (1- (Vs/V) )

2) f=f' ( (V +or- Vo) / (V +or- Vs) )
for the top set you use + if the detector moves toward the source
use - if the detector moves away from the source
for the bottom set, you use + if the source moves away from the detector
use - if the source moves towards a detector

For both equations V= speed of sound
Vo =speed of sound at observer (detector)
Vs = speed of sound from source


I was taught using the second equation by TPR, but it seems like the first equation would be easier since you don't have to memorize all the conditions of whether to use the plus signs or minus signs. However, I am worried that maybe the top first equation is not accurate.

Any physics whiz want to help me?

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[MundaneMD]

The equations you wrote are both wrong, but I'll explain that in the end. But first, I'll derive equation 2 from equation 1 to show that the two equations are the same.

1) f' = f x (1 + (Vo/V)) / (1 - (Vs/V)

Multiply the whole equation by V/V.

f' = f x V x (1 + (Vo/V)) / (1 - (Vs/V))

Simply by distributing the V.

2) f' = f x (V + Vo) / (V - Vs)

--------------------------------------------

Now, the actual equation for the Doppler Effect is:

f' = f x (V ± Vo) / (V Ŧ Vs)

(You had only + and -)

Unfortunately, you will have to remember when to use the plus or minus signs for any Doppler Effect problem. But you won't necessarily have to memorize the different situations. You can use logic to determine which signs go where.

I'm terrible at explaining things, so I won't even attempt to explain how to determine the signs. I'll probably end up confusing you, and myself as well. I'll leave that up to a real physics whiz. 😛

 

[Corpus Callosum]

I have two conflicting equations used to solve the doppler effect. Which one is correct, or can you use both of them?

1) f=f' ( 1+ (Vo/V) ) / (1- (Vs/V) )

2) f=f' ( (V +or- Vo) / (V +or- Vs) )
for the top set you use + if the detector moves toward the source
use - if the detector moves away from the source
for the bottom set, you use + if the source moves away from the detector
use - if the source moves towards a detector

For both equations V= speed of sound
Vo =speed of sound at observer (detector)
Vs = speed of sound from source


I was taught using the second equation by TPR, but it seems like the first equation would be easier since you don't have to memorize all the conditions of whether to use the plus signs or minus signs. However, I am worried that maybe the top first equation is not accurate.

Any physics whiz want to help me?

You don't have to memorize anything, all you need to know is the following:
*when a source is approaching, you know that the frequency will be higher (assume stationary detector), since freq higher, then denominator will be smaller, now what makes denominator smaller, smaller number, which means you subtract not add in the denominator, to make it a smaller number and hence it would be -Vs in the denominator.
*Second case, moving away, exactly the opposite reasoning, add (+) both velocities in the denominator to make it bigger and thus make observed freq smaller.
If the detector is not stationary, you use the opposite sign velocity in the numerator from the one you used in the denominator, your objective is to make the ratio (freq) bigger or smaller respectively in my examples; in other words if you subtracted in the denominator because the source is moving towards the detector, you add the detector velocity in the numerator and hence the observed freq would increase, exactly what you'd expect when a source is approaching.
If you understood the above explanation, you will be able to tackle any doppler effect problem with minimal time and best accuracy.Don't memorize anything, just think. On the mcat, first of all, they won't give you this formula, and second you don't have time to analyze it too much. You have to reason along those lines I explained to you.
Good luck.

 

[Sarahgelatinano]

Thanks to both of you! I think I will do some practice problems and try to use the logic 🙂