Easy Doppler Effect Question

[TheJourney]

So I'm having trouble utilizing the equation. I can't seem to know when to add or subtract the velocity of the source or observed to v. First off, this is the correct equation correct, f = f ' ((V +/- Vs)/(V +/- Vo))? Which seems to be often rewritten to f ' = f ((V +/- Vo)/(V +/- Vs)).

Here's the question:
A police car moving toward a stationary pedestrian at a speed of 10 m/s operates its siren. If the pedestrian perceives the frequency of the siren to be 1030 Hz, what is the frequency emitted by the siren?

A. 10 Hz
B. 100 Hz
C. 1000 Hz
D. 10,000 Hz

I got the answer right (C, 1000 Hz), but mostly because the numbers were so far apart.
I set up the equation as follows: f = 1030 (350/340). However this would mean the emitted frequency is higher than 1030 Hz, but it should be lower. Where am I making the mistake, thank you in advance.

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[NextStepTutor_1]

So, you are mostly correct in setting up the values, however, you might be getting confused because you are mixing up the reference points when you are doing your calculation. I find it easiest to use the equation f (observed) = f(emitted) * (V+/- Vs)/(V+/-Vo) because the MCAT will generally ask you from the reference point of the observer. Now, just look at the equation just using the concepts. If the observer is standing still and the source moves towards it, does frequency go up or down? It goes up! So the only way that occurs in the equation above is if you add the velocity of source. So, when the source travels towards the observer, you add, and when it travels away, you subtract. Now, lets imagine that the source stayed the same and the observer moved. If the observer moves away, does the frequency increase or decrease? It decreases! So the only way that occurs is if you add V0. So when the observer moves away, you add, and when it moves towards, you subtract.

Now let's try that for this problem, we get that the source is moving towards and the observer is still:

1030 = (f emitted) * (340 + 10) / (340 + 0) <== Here is where you messed up, you plugged in the wrong values for f and f'.

f emitted = 1030 * (340/350) = 1000 Hz.

Hope that helps!

 

[TheJourney]

So, you are mostly correct in setting up the values, however, you might be getting confused because you are mixing up the reference points when you are doing your calculation. I find it easiest to use the equation f (observed) = f(emitted) * (V+/- Vs)/(V+/-Vo) because the MCAT will generally ask you from the reference point of the observer. Now, just look at the equation just using the concepts. If the observer is standing still and the source moves towards it, does frequency go up or down? It goes up! So the only way that occurs in the equation above is if you add the velocity of source. So, when the source travels towards the observer, you add, and when it travels away, you subtract. Now, lets imagine that the source stayed the same and the observer moved. If the observer moves away, does the frequency increase or decrease? It decreases! So the only way that occurs is if you add V0. So when the observer moves away, you add, and when it moves towards, you subtract.

Now let's try that for this problem, we get that the source is moving towards and the observer is still:

1030 = (f emitted) * (340 + 10) / (340 + 0) <== Here is where you messed up, you plugged in the wrong values for f and f'.

f emitted = 1030 * (340/350) = 1000 Hz.

Hope that helps!

Hey, thanks for your response and thank you for clarifying that add and subtract, it helped!

Two questions, one, comparing your equation to the one I wrote, my equation was written incorrectly, right?
Second, rewriting the equation to isolate the source frequency yields, f = f" * (V +/- Vo)/(V +/- Vs)?

 

[NextStepTutor_1]

Your equation might have been correct, I think you might have just plugged in the numbers into the wrong f values. The f and f' threw me for a loop because they weren't really specific as to what they referred to.

Yes, the second equation you wrote is correct!

 

[TheJourney]

Thanks again, I just repeated a few problems using what you said and it made things a lot easier. I appreciate it!!

PS: In the original post f = source, f' = observer. I did have the equation mixed up :/