# The Doppler Effect (in general)

1. Jul 16, 2009

### Urmi Roy

I have a problem in regard to the doppler effect,which may be generalised to all waves--sound,water etc.

Please explain why the observed frequency increases as the object approaches an observer and then decreases as the object passes the observer.Actually,I thought that since doppler effect depends only on the relative velocity between observer and source,the observed frequency should be constant throughout the process,as the relative velocity does not change as the distance between the source and observer changes.

I also found on a website that it said that 'the observed frequency of an approaching object declines monotonically from a value above the emitted frequency, through a value equal to the emitted frequency when the object is closest to the observer, and to values increasingly below the emitted frequency as the object recedes from the observer'---Does this mean the same thing as what I asked at the begginning or is it different?

Also,does the intensity of the sound increase as an object approaches an observer and decrease once it passes and recedes from the observer?

2. Jul 16, 2009

### tiny-tim

I think you're assuming that the object is heading straight for the observer.

In practice, it usually misses the observer, and so the relative speed does change continuously.
Yes.

3. Jul 16, 2009

### Staff: Mentor

The relative velocity certainly changes: You start out moving toward the source and end up moving away from it.

4. Jul 16, 2009

### DeepSeeded

Well lets say it was heading stright for the observer, and the observer could see both forward and behind. He is right, relativley there is no difference, the doppler effect collapses...

5. Jul 16, 2009

### Staff: Mentor

Not quite. See my response above.

6. Jul 16, 2009

### DeepSeeded

However, in both cases the light is always heading towards the observer after being emitted from the object.

7. Jul 16, 2009

### Staff: Mentor

So? The light/sound always moves toward the observer (relatively) otherwise you won't see/hear anything.

What matters for the Doppler effect is your velocity relative to the source. In one case you move towards the source; in the other, you move away. Big difference.

8. Jul 16, 2009

### DeepSeeded

O well, it was fun while it lasted :)

9. Jul 16, 2009

### vin300

Oh ho Doc, say yours is the reference frame. The velocity of the train is as it is after it passes you

10. Jul 16, 2009

### HallsofIvy

I think Doc Al and tiny tim are talking about different situations. tiny tim is talking about a situation where the motion of the source of sound is slightly off to one side of the observer, the velocity is continuously changing so the frequency heard is continuously changing. That is also my interpretation of the original question. If the source is moving directly toward the observer, the frequency is constant (above that of the emitted signal) until the source passes then suddenly drops below the frequency of the emitted signal. That is the situation Doc Al is referring to. Note that in the first case, while the change in frequency is continuous, it is not linear. There will be relatively little change in the frequency when the source is farther off, most change when the source is nearest. That effect increases when the point of "closest approach" to the observer is closer to the observer- that is when the source just misses the observer.

11. Jul 16, 2009

### tiny-tim

It is as it is, is it? Or is it after being as it is, that it is?

12. Jul 16, 2009

### Staff: Mentor

In this context, "relative velocity" refers to the radial component of the rate of change of the position vector of the source with respect to you (the observer). As the source approaches, the length of that vector is decreasing; as the source recedes, its length increases.

13. Jul 16, 2009

### DeepSeeded

Wait a minute, with light it doesnt matter what your relative velocity is, light is only one speed c, invariant. So... If you had a light emitting diode travelling to you, then away from you, whats the difference? The light is traveling at speed c to you at all times.

Next time I get pulled over I know what my argument is going to be. "Its only a 4 cylinder" isnt working anymore.

14. Jul 16, 2009

### Staff: Mentor

Again, it's the speed of the source that matters, not the speed of the light. Same thing with sound: In still air, the speed of sound with respect to a stationary observer will be the same, regardless of the speed of the source. (In fact, that was the example that started this thread.)

15. Jul 16, 2009

### Urmi Roy

I was not aware of any difference between relative motion when the source of sound is slightly off to one side of the observer and when they are not.

What is the cause for this difference?

What I originally meant to say is that the observed frequency continuously changes even when the source and observer are moving toward eachother,and separately when they are moving away from eachother,and also that at the point of closest approach,the observed frequency equals the real frequency.

Doc Al said that the observed frequency changes only when the relative motion changes from 'moving toward' to 'moving away'---that's understandable,but I came accross a source which said that the observed frequency changes continuously during the interval that the source and observer move toward eachother and also during the interval that they move away from eachother.
This is what I don't understand--on these individual intervals,there is no change in relative velocity of 'moving toward' or 'moving away'.

Again at the point of closest approach,there is still relative motion between source and observer,so shouldn't there be a different observed freqeuncy even here?

This seems to confirm that the observed frequency does indeed change continuously during the 'moving towards eachother' part and then separately on the 'moving away from eachother' part,and that the observed frequency is in some way related to the 'distance between the source and observer.
I really don't understand it!!

16. Jul 16, 2009

### Urmi Roy

Is this the same thing that I found on the wesite that said 'the observed frequency of an approaching object declines monotonically from a value above the emitted frequency, through a value equal to the emitted frequency when the object is closest to the observer, and to values increasingly below the emitted frequency as the object recedes from the observer'??

17. Jul 17, 2009

### vin300

The doppler effect as you think holds in the ideal condition that the relative velocity is the same throughout, but in real cases it becomes a monotonically decreasing curve.
The doppler effect would be as you thought if you stood on linear track of an approaching train with constant velocity and the train went through you, but you stand by the side and the component of velocity vector towards you goes on decreasing and becomes zero when closest to you and agin goes on increasing like the velocity vector of a parabolic curve when a ball is thrown up, if you were to see it facing perpendicular to the earth in the air at the point of 0 velocity.
The formulae still hold true but there is change in frequency as there is change in velocity.

Last edited: Jul 17, 2009
18. Jul 17, 2009

### Staff: Mentor

If the source is moving directly towards you, then the observed frequency is shifted but steady; similarly, if the source moves directly away from you. In such a case the observed frequency doesn't continually change.

Of course, that situation is unrealistic. Usually, the source doesn't come directly at you, otherwise you'll be hit. It passes by you. If you imagine a line drawn from you to the source, the length of that line--which represents the distance between the source and observer--changes as the source approaches you (at an angle), passes by you, and then recedes from you. The rate of change of that distance is the "relative velocity" that we are concerned with. That rate of change varies continuously as the source moves.

The only relative motion that counts (for the non-relativistic Doppler effect, at least) is motion toward or away from the observer. At the point of closest approach the source is moving sideways with respect to the observer, thus the radial velocity (the rate of change of the distance between source and observer) is momentarily zero. At that moment the source is neither getting closer or farther from the observer.

19. Jul 17, 2009

### Urmi Roy

I suppose that when the source and observer are in the process of moving past eachother,starting from a certain distance,there must be some component of the relative velocity which is continuously changing,resulting to the continuously changing observed frequency.Which component is that?

I'll probably understand this better,if I know exactly how a particular component of the relative velocity changes continuously.

20. Jul 17, 2009

### Urmi Roy

I suppose to track the continuously changing observed frequency,one would have to apply the same formulae separately for every instant of the motion,right?

21. Jul 17, 2009

### Staff: Mentor

If you put the observer at the center of a polar-coordinate system, you use the radial component of the source's velocity.

22. Jul 17, 2009

### cepheid

Staff Emeritus
Well you can just draw a picture. Let's say you, an observer, are located a distance d away from a track (d is your perpendicular distance from the track).

Let's say a train is coming towards you (along the track, of course), and is distance x away from you (in the along the track direction). This means that your actual distance, r, from the train (i.e. the line of sight distance) is given by the hypotenuse of the right triangle:

r = (x2 + d2)1/2

Your line of sight to the train makes an angle θ with the track, where we have:

tanθ = d/x

cosθ = x/r

sinθ = d/r

Now, if the train is moving with speed v along the track (i.e. in the x-direction), then you can resolve this velocity into a component that is parallel to the line of sight (i.e. radial, i.e. toward the observer) and a component that is perpendicular to the line of sight (i.e. tangential). It is clear from the picture that the line of sight component is given by:

v|| = vcosθ = vx/r = (vx)/(x2 + d2)1/2

This makes sense because when x > 0, the line of sight component is toward the observer but is decreasing, and so and the frequency is continuously decreased. I guess it would go roughly linearly with x for |x| << d). When x = 0 (the train is at the point right beside you on the track), there is no component of the velocity toward the the observer, and hence the frequency is unshifted at this instant. When x < 0, the line of sight component of the velocity is now away from the observer, and the Doppler shift switches direction.

So your quote from that website was correct. The frequency will vary continuously from being higher than the emitted frequency to lower than the emitted frequency (obviously passing through the emitted frequency along the way).

23. Jul 17, 2009

### Urmi Roy

Wow!!!! That was an excellent and rather simple explanation cepheid!

We can infer from this that the observed frequency will first start to reduce, being the greatest at the point that the whistle of the train is first perceived and slowly passes the real frequency,followed by a gradual decrease until the train's whistle is no longer heard.

Also, this variation follows a parabolic nature, just like the cosine function varies between
-90 and +90 degrees,right?

May I also ask that in the case that the observer is standing on the train's track (this is just a thought experiment!) and the train passes through the observer,the frequency must change abruptly as it drops from a fixed frequency higher than the real frequency (while moving towards the observer) to a frequency equal to the real frequency when it approaches the observer,and vice versa as it finally moves away??

24. Jul 17, 2009

### DaveC426913

Yes. Remember that, while sound is perceived as a continuous input, it is actually "granular" in that it oscillates. It is the oscillation that produces the sound. Because of this you could indeed have an apparently instant drop in frequency - the duration of the drop is smaller than the granularity of the sound itself.

At the finest detail, you would measure the motion of the train on a scale that is smaller than the wavelength of the sound.

At some point, the horn/loudspeaker will reach the peak of its compression phase while the train is still coming toward you, yet the next peak will not arrive at the observer's location until after the train has passed. That means the frequency will have dropped froim high to low in one single cycle.

25. Jul 18, 2009

### vin300

Yes. applications