The Doppler Effect (in general)

[DrGreg]

I think this thread is getting bogged down in the technicalities of how to measure a non-constant frequency, which has little to do with the doppler effect.

Mathematically, signal of frequency f can be described by the formula

$$\sin (2\pi f t + \phi)$$​

and that is valid whether f is constant or varies as a function of time. The doppler effect can be described mathematically in these terms and "granularity" is irrelevant.

The complication arises in the real world if you are given a signal to listen to and asked to decide what f is. This is difficult because because you won't just hear the signal but also interference from other sounds nearby. If you analysing using a microphone and electronic equipment (analogue or digital), there will be distortions and noise introduced by the equipment. If you analysing with your own ears and brain, there will be distortions due to the acoustic properties of the ear and its perception mechanisms. The problems get worse if you can listen over only a short period of time or the frequency is changing very rapidly. This means in practice there are always uncertainties when trying to measure the frequency of a signal over a short period of time or the when frequency is changing very rapidly. (Mathematically, this uncertainty is pretty much identical to the Heisenberg uncertainty of quantum physics.) However, I wouldn't describe this as "granularity" as that suggests only discrete answers and the problem is a bit more subtle than that. It is a practical problem of measurement and doesn't affect the theory behind the doppler shift, where we can assume no noise or interference and perfect measurements (even if such measurements are impossible in the real world).

 

[Pumblechook]

It you receive signals from orbital satellites the frequency change is real enough, not just an illusion.

If you are using a satellite relay it is possible to reduce the doppler shift particularly if the up-link and down-link are on close frequencies.

 

[Urmi Roy]

Right,I understand.
I think I'll stick to the basic doppler theory,as DrGreg suggested.

 

[Urmi Roy]

The only relative motion that counts (for the non-relativistic Doppler effect, at least) is motion toward or away from the observer.

I was studying about the relativistic doppler effect a few days ago and what I understood is that it is basically the same as classical doppler effect,but Einstein slightly modified it to accommodate to Maxwell's theory of the constancy of the speed of light.

Now,is there any other basic point I'm missing out here---especially from what Doc Al said?

 

[Doc Al]

With the relativistic Doppler effect, you'll also get a frequency shift when the radial velocity is zero (at the distance of closest approach, in your original example) due to time dilation. This is called the transverse Doppler effect.

 

[vin300]

With the relativistic Doppler effect, you'll also get a frequency shift when the radial velocity is zero (at the distance of closest approach, in your original example) due to time dilation. This is called the transverse Doppler effect.

I don't think so. The radial velocity remains zero and without velocity there is no doppler shift

 

[Doc Al]

I don't think so. The radial velocity remains zero and without velocity there is no doppler shift

Just because the radial component of the velocity is zero does not mean that the velocity is zero. There is still a tangential (transverse) component.

 

[Urmi Roy]

Is the whole picture in relativistic doppler effect similar to that of the classical doppler effect,(especially reffering to post no.22 by cepheid)----only that in this case we can have a train moving towards us which has a bright headlight,and consider time dilation?

In other words,at which point in cepheid's description do we have to bring in time dilation?

 

[Doc Al]

In other words,at which point in cepheid's description do we have to bring in time dilation?

cepheid's post #22 was an explanation of the radial component of velocity, not a derivation of the Doppler effect. In deriving the relativistic Doppler effect, time dilation comes in when describing the frequency of the source, since in the frame of the observer the source frequency must be adjusted due to time dilation by the Lorentz factor γ.

For a description of the relativistic Doppler effect, see: http://en.wikipedia.org/wiki/Relativistic_Doppler_effect" .

 

[Urmi Roy]

I went through the wikipedia article and I think understand now.

In relativistic doppler effect, the frequency is perceived to be different from what one would expect from the classical doppler effect because the time interval that one would calculate from the classical doppler effect itself is time dilated,and so the perceived frequency is now different.

However, I didn't really find myself comfortable with the 'Transverse doppler effect' and I'm not sure that I need to be.

Since time dilation is not restricted to any particular direction,as is length contraction,I don't think that the observation of the doppler effect,should be affected by the angle from which the observer is looking.This must also mean that the discussions that took place about the classical doppler effect in the previous pages--like the different situations that arise when an observer is standing on the path of the moving source,or when he is standing to the side of it--must also be applicable to the relativistic doppler effect.

Am I okay here?

 

[vin300]

You can apply length contraction in the wavelength to the derivation and find that the result is fine. The coordinate axes bend and at the point of closest approach, both its components are actually away from the obsever for relativistic speeds.There is stil apoint where radial velocity is zero but since the transverse is not perp the resultant stands not to be 0

 

[Urmi Roy]

The coordinate axes bend and at the point of closest approach, both its components are actually away from the obsever for relativistic speeds.There is stil apoint where radial velocity is zero but since the transverse is not perp the resultant stands not to be 0

Please could you elaborate more on this point?

 

[vin300]

You could see in the simulation bending of grids. That essentially explains it. The grids distance in front of the observer and come close at the back so the same length forward is measured lesser and backward is more.Apply to wavelength this explains doppler shift
The components mutually perp will now reduce the inclination
Note that the velocity is still same inverse change in frequency.The components change magnitude and direction at the same distance from outside observer in the orig eg

 

[Urmi Roy]

The bending of grids portion in the wikipedia article is due to aberration,whereas the usual red shift- blue shift is due to the doppler effect.If we ignore the aberration and discuss only the results of the doppler effect,how much will they be affected by the direction of relative motion?

As Doc Al stated,there is still a frequency shift when the source and observer at the point of closest aproach(their relative velocity is transverse in this case) ,due to time dilation----is this the so called 'tansverse doppler effect'?

 

[vin300]

There is still a problem The grids do not distort in the outside observer's reference, so the components are mutually perp for him The velocity at the closest point proves to be 0

 

[Capt. McCoy]

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.)

I think what doc as is trying to say here is there that in a doppler effect, there are various movements, (1) movement of the source of the energy (light/sound), (2) the movement of the energy itself.

 

[vin300]

I think what doc as is trying to say here is there that in a doppler effect, there are various movements, (1) movement of the source of the energy (light/sound), (2) the movement of the energy itself.

That's alright, but doc said the velocity at the closest point is not zero but as I see it there is no change in the direction in which the components point so no contribution of transverse velocity anywhere along the process (always perp to long vel)

 

[Doc Al]

As Doc Al stated,there is still a frequency shift when the source and observer at the point of closest aproach(their relative velocity is transverse in this case) ,due to time dilation----is this the so called 'tansverse doppler effect'?

That is correct.

That's alright, but doc said the velocity at the closest point is not zero but as I see it there is no change in the direction in which the components point so no contribution of transverse velocity anywhere along the process (always perp to long vel)

Answer this: At the point of closest approach, is the source moving with respect to the observer? If so, time dilation (and the associated "transverse Doppler shift") applies.

 

[Capt. McCoy]

That's alright, but doc said the velocity at the closest point is not zero but as I see it there is no change in the direction in which the components point so no contribution of transverse velocity anywhere along the process (always perp to long vel)

it's not zero because basically (from what you said also) it's just the closest point...not the point itself...

 

[Urmi Roy]

it's not zero because basically (from what you said also) it's just the closest point...not the point itself...

At the point,then,there is no doppler effect at all,right?

This must be the same for sound waves also.

 

[Urmi Roy]

I was going through the wikipedia article about the doppler effect and it said that "The Doppler effect is time-dependent in general (thus we need to know not only the source and receivers' velocities, but also their positions at a given time."

What does this mean?

 

[Doc Al]

I was going through the wikipedia article about the doppler effect and it said that "The Doppler effect is time-dependent in general (thus we need to know not only the source and receivers' velocities, but also their positions at a given time."

What does this mean?

If you are at rest and all you know is that the source is moving at a given velocity (10 m/s north, say), how can you determine the expected Doppler shift? You need to know whether the source is north, south, east, or west of you. In general, position matters.

 

[Urmi Roy]

You need to know whether the source is north, south, east, or west of you. In general, position matters.

Direction does come in when we're just trying to get the details of the situation under dicussion,but it doesn't affect the results.

Whether we have our source moving away at 10m/s north,or south ,or in any direction,the observation is the same.

Also,in regard to the position,besides the fact that objects farther away look smaller,it doesn't affect the doppler effect---its theory and observations.

Is that right?

 

[Doc Al]

Whether we have our source moving away at 10m/s north,or south ,or in any direction,the observation is the same.

You're the one who read the Wiki article. Did they meaning radial velocity with respect to the observer or just velocity. (Let's not go another 10 pages based on ambiguity.)

If you to discuss the statement in the wiki article, then post a reference.

 

[vin300]

Direction does come in when we're just trying to get the details of the situation under dicussion,but it doesn't affect the results.

Whether we have our source moving away at 10m/s north,or south ,or in any direction,the observation is the same.

So you didn't understand all the concept of radial velocity
It's the component of velocity towards you(vcos(angle)) that is added to c and causes the traditional doppler effect, and the actual relative velocity appears in the lorentz factor causing relativistic effect
Derive, you get the result as fo={1-[vcos(angle)/c]}*f*gamma
Now this formula can be put in another way, using the aberration formula
It happens because at high speeds the angle at which the wave is sent to the velocity decreases, can be well explained by bending of grids
If you study the grids, the components vcos(angle) and vsin(angle) which were mutually perp decrease inclination but this does not mean they contribute to each other because the grids are themselves bent

 

[Urmi Roy]

I wasn't talking about the 'radial' or 'transverse' direction----we can have these components of relative velocity whatever direction(north,south,east) the motion is in.

I was actually reffering to the importance of 'position' of source and observer in the analysis.Besides,as long as we know the relative velocity,and the direction of it,it doesn't matter whether it's north or south,what matters is the direction w.r.t each other (moving towards or moving away)--we can choose north-south directions as we please.

The line I'm referring to is on the page given below,in the third last paragraph of the section 'Analysis'.

http://en.wikipedia.org/wiki/Doppler_effect

 

[vin300]

Time reversal?Iwould wwant to know more on it

 

[Doc Al]

I wasn't talking about the 'radial' or 'transverse' direction----we can have these components of relative velocity whatever direction(north,south,east) the motion is in.

I was actually reffering to the importance of 'position' of source and observer in the analysis.Besides,as long as we know the relative velocity,and the direction of it,it doesn't matter whether it's north or south,what matters is the direction w.r.t each other (moving towards or moving away)--we can choose north-south directions as we please.

The line I'm referring to is on the page given below,in the third last paragraph of the section 'Analysis'.

http://en.wikipedia.org/wiki/Doppler_effect

That wiki paragraph is referring to the fact that in a more complete analysis one must take the travel time of the signal into account (from source to observer) in order to determine what the observer actually observes at any given time. To do that requires knowing the position of the source at the time of emission, not just its direction of motion.

 

[Urmi Roy]

Thanks,Doc Al,I understand now.

 

[vin300]

Waves farther from the source lag behind those closer to it.So if you have positive radial velocity greater than the speed of sound you hear the song played backwards
That's time reversal