# Doppler Effect

1. May 16, 2013

### Knightycloud

1. The problem statement, all variables and given/known data
A car with a horn making a frequency of 'f' Hz is driven in a circle with a radius of 'r' m. The uniform velocity of the car is v ms-1.
Draw graphs showing the frequency observes by the observer who is standing on;
a) Position A
b) Position B

(Position B is very far from the circle)

2. Relevant equations
f' = f($\frac{u}{u\pm v}$)

u - Velocity of sound
v - Velocity of the car

3. The attempt at a solution
My answer for this one is only the position A is having a variation in the frequency while the position B observes the same frequency of 'f' Hz

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2. May 16, 2013

### haruspex

When at position B, is the car a constant distance from the observer? If not, it must be sometimes moving towards the observer and sometimes away.
I suggest you should show the position of the car on the horizontal axis of the graphs, e.g. in terms of theta, where the car's position is at (r, theta) in polar coordinates centred on the centre of the circle. The comparison between the two graphs is interesting.

3. May 16, 2013

### Knightycloud

Nope, both positions A & B are at constant distances and they're not moving either. So you mean both positions observe a variation in the frequency regardless how far they're from the source?
And is that graph I drew correct???

4. May 16, 2013

### haruspex

No, you misunderstand my question. When the observer is at position B, is the car at constant distance from the observer?
Yes.
Yes, but you need to mark the x axis to show which point on the graph corresponds to which position of the car.

5. May 17, 2013

### Knightycloud

No the car keeps moving and the observer is still.

Am I correct if I say, both positions plot the same graph with same values? I mean in the doppler equation, only variables are the velocities and the frequency. There's no mention about how far the observer is from the object.

6. May 17, 2013

### haruspex

No, the graphs are similar but not the same. For one thing, the peaks and troughs don't line up, which is why I believe you must show the x-coordinates for a proper comparison.
If I were doing this problem I would develop the actual equations, but from the way the question is worded I feel they don't expect you to do that. Instead, you need to sketch the graphs from simple reasoning.
Denote the position of the car by theta as I described in an earlier post. So when the car is near A theta = 0, and when it's furthest from A theta = pi. With the observer at A, for what theta(s) is the observed frequency:
- highest?
- lowest?
- same as emitted frequency?
- changing most rapidly?
Same questions at B.

7. May 17, 2013

### Knightycloud

I've changed the graph accordingly. Is it correct now? :)

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8. May 17, 2013

### haruspex

B is about right, but A is significantly off. At what theta will the car be traveling straight towards A?
Here's a question I missed before: The peak observed frequency will be when the car is moving straight towards the observer, right? Does the distance affect this?

9. May 18, 2013

### Knightycloud

So that means if I draw a tangent to the circle from the point B, that is the moment when the car is moving straight to the point and that's when the highest frequency is observed?

10. May 18, 2013

### Knightycloud

And another thing, Are these both positions observe the same highest frequency? Or is it differs?

11. May 18, 2013

### haruspex

Yes, and the lowest if moving away.
You quoted the formula in the OP. Does distance figure in it?

12. May 18, 2013

### Knightycloud

Ok then, From what I understood, the highest frequency observed is the same for both positions and the only difference is 'the time (In this case; θ)' when they observe it. Right? If I'm correct here this one's settled!!! :D

13. May 18, 2013

### haruspex

The shape is also rather different. In particular, for what thetas are the highest and lowest frequencies heard at A?

14. May 19, 2013

### Knightycloud

Yea the shapes are different! But the peaks and bottoms are at the same values, right?

15. May 19, 2013

### haruspex

The same heights, yes, not the same theta values. What is the most striking difference?

16. May 19, 2013

### Knightycloud

Difference is the start point and the end point of a cycle.

17. May 20, 2013

### haruspex

Too vague. Please either post a picture or try to be a lot more descriptive.

18. May 20, 2013

### Knightycloud

Is this one the correct graph???

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19. May 20, 2013

### haruspex

No, the shape is significantly different in the A case. Pls try to answer this question I keep asking you: at approx what values of theta will the frequency be highest and lowest at A? Remember, since the speed is constant, this depends entirely on the extent to which the motion is towards or away from A.

20. May 21, 2013

### Knightycloud

Draw two tangents to the circle from point A. One tangent represents the car coming in and the other one represents the car going out. That is when the highest and the lowest are observed. Theta values are -θ and +θ where theta is measured taking AO as the base.

Am I close enough?