Help with understanding the Doppler effect

[Dale]

The abstraction there is next: if medium exist then Doppler's effect can define motion in this medium regardles of the inertial frames, and this is me calling 'an absolute'.

I mentioned above the negative connotation of the term absolute above. What you are describing as "absolute" is not the meaning generally ascribed to that term by the rest of the community. By using that term where it does not apply you are being deliberately offensive: going out of your way to use a provocative term that is neither appropriate nor necessary.

 

[frostysh]

It really isn't. You just need to keep track of the velocities of the source, medium, and receiver in whatever frame you want to work in.

No I don't, I simply measure the difference in wavelengths in the rest case of the source and in my case, and the end, I know what is moving what is not — this difference is an invariant. This invariant will be the same in the any other inertial systems.

So, if you look at the link I sent you will see that the general Doppler effect is given by $$\frac{f_a}{f_e}=\frac{1-v_a/c_s}{1+v_e/c_s}\sqrt{\frac{1-(v_e/c)^2}{1-(v_a/c)^2}}$$ where I am using the notation in that paper except for the substitution $\nu=f$ which I use because $\nu$ is visually hard to distinguish from $v$ for me in most fonts, particularly the one in that paper.

If we make the simplifying assumptions $v_a<c_s<<c$ and $v_e<c_s<<c$ then we can solve the simplified formula for $v_e$, giving $$v_e=\frac{f_e}{f_a}(c_s-v_a)-c_s$$ so assuming that $f_e$ and $c_s$ are known a priori then measuring $f_a$ still does not give enough information to determine $v_e$, we also need to know $v_a$ independently somehow.

If you don't make the simplifying assumptions then the same reasoning applies, but I think that there is not a closed form solution and you have to numerically solve it.

Cool formulas, but the first one I have very poorly barely understand, the second one no giving any physical explanations, if looking just on mathematics of this formula we will not understand that corresponding to the interiatl frames of observers the wavelength is an invariant. Of course in terms of mathematics and unknown terms this equation no different from the other in case of solving it, if too many unknows we cannot resolve it.

And by the way, usually peoples describing what symbols have what meanings in formulas, because can be missunderstandings... What is means of $c_{s}, f_{e}, v_{a}, f_{a}$?

I mentioned above the negative connotation of the term absolute above. What you are describing as "absolute" is not the meaning generally ascribed to that term by the rest of the community. By using that term where it does not apply you are being deliberately offensive: going out of your way to use a provocative term that is neither appropriate nor necessary.

How do you to name the effect that can be used to destroy the equallity of inertial frames of references?

 

[Ibix]

This invariant will be the same in the any other inertial systems.

Just like the wind speed your observer would measure. Everyone will agree his measurement, and everyone will agree that it is his speed relative to the medium. That doesn't make the rest frame of the medium special.

How do you to name the effcet that can be used to destroy the equallity of inertial frames of references?

A misunderstanding of what you are doing.

 

[frostysh]

Just like the wind speed your observer would measure. Everyone will agree his measurement, and everyone will agree that it is his speed relative to the medium. That doesn't make the rest frame of the medium special.
A misunderstanding of what you are doing.

The problem is that wavelength is not relative to the frame of reference like speed of the wind... (Cannot find facepalm smile.) The invariant is something that is not changing due to change of intertial frame. The speed of wind will change, this is not an invariant.
The speed of wave propagation in medium is an invariant to any inertial frame too, because it's a very property of medium itself. What about your wind?

 

[A.T.]

Doppler's effect exist and it is reality, relativity exist, and this is reality too, but they cannot coexist in the same time in the same model,

Sure they can. And your word games don't change that.

 

[A.T.]

The speed of wave propagation in medium is an invariant to any inertial frame

"In medium" already defines the frame relative to which the speed is measured in, so adding 'to any inertial frame' makes no sense, and is just gibberish.

 

[frostysh]

Sure they can. And your word games don't change that.

This is more philosophical question but as you saw, the Doppler's effect is invariant and clearly showing which frame moving, which not. So in this terms 'rest' and 'moving' is not relative, if you can make such an abstraction, you can and model think as a whole Universe is filled by some medium — the end of relativity then in this model, but of course it is not true, the vacuum is not a medium (obviously) and no any 'ether' observed during hundred of years so the relativity rulezz.

 

[Ibix]

The problem is that wavelength is not relative to the frame of reference like speed of the wind

However, both measured frequency and wave speed (relative to the reference frame, not the medium) are frame dependent. Thus there is no problem with changing inertial frames - as long as you remember to transform all relevant physical quantities.

The speed of wave propagation in medium is an invariant to any inertial frame too, because it's a very property of medium itself.

The speed relative to the medium is invariant, sure. The speed relative to the frame isn't.

What about your wind?

The speed of the wind relative to itself is zero always - an invariant just like the speed of sound relative to the medium. The speed of the wind relative to the frame is frame dependent, of course, just like the speed of sound relative to the frame.

 

[A.T.]

Doppler's effect is invariant and clearly showing which frame moving, ...

... moving relative to the medium.

 

[Dale]

Cool formulas, but the first one I have very poorly barely understand, the second one no giving any physical explanations, if looking just on mathematics of this formula we will not understand that corresponding to the interiatl frames of observers the wavelength is an invariant.

The wavelength is not an invariant, and in any case if $v_a\ne 0$ then I am not sure how the absorber can measure the wavelength. What formula are you using for that?

Of course in terms of mathematics and unknown terms this equation no different from the other in case of solving it, if too many unknows we cannot resolve it.

Yes, that is the point made by @A.T. and myself earlier in the thread.

And by the way, usually peoples describing what symbols have what meanings in formulas, because can be missunderstandings... What is means of $c_{s}, f_{e}, v_{a}, f_{a}$?

The meanings of the symbols is described in the paper that I linked to as I explicitly stated "where I am using the notation in that paper" with one exception which I described above.

How do you to name the effect that can be used to destroy the equallity of inertial frames of references?

It doesn't matter because this is not such an effect. By trying to use that name where it does not apply you are being deliberately and inappropriately provocative.

 

[frostysh]

However, both measured frequency and wave speed (relative to the reference frame, not the medium) are frame dependent. Thus there is no problem with changing inertial frames - as long as you remember to transform all relevant physical quantities.

The speed relative to the medium is invariant, sure. The speed relative to the frame isn't.

The speed of the wind relative to itself is zero always - an invariant just like the speed of sound relative to the medium. The speed of the wind relativet to the frame is frame dependent, of course, just like the speed of sound relative to the frame.

The speed of wind is not connected to the wavelength of wind, and wavelength is and invariant. Do you understand that wavelength is the same as mass, as volume, I don't know, as the time interval in the classical mechanics? At least me understand this (if I am wrong, correct me). So your wind is useless analogy...

... moving relative to the medium.

Omg... And to which your medium is relative? To observer inertial frame? To source? — There is Galelean transformation, the end of story. Speed of source relative to the medium (not the speed of medium relative to the source) changing the very invariant, what do you not understand?

The wavelength is not an invariant, and in any case if $v_a\ne 0$ then I am not sure how the absorber can measure the wavelength. What formula are you using for that?

Very please, read the page two few sentences — Galilean Transformation of Wave Velocity. Do you anderstand which is means 'invariant'? This is a very fundamental thing (I mean Galelean transformation), you can scribe your formula but it's meneangles because the basis of your formulas is that very transformation, actually in the article case only of the moving observe, but it's no matter.

The meanings of the symbols is described in the paper that I linked to as I explicitly stated "where I am using the notation in that paper" with one exception which I described above.
It doesn't matter because this is not such an effect. By trying to use that name where it does not apply you are being deliberately and inappropriately provocative.

Okay, not problem.

 

[Ibix]

The speed of wind is not connected to the wavelength of wind

Wind does not have a wavelength.

So your wind is useless analogy

I think you don't understand my point. Measuring the speed of the wind simply tells you your speed relative to the medium, whether you regard yourself or the medium or both as moving. That measurement is invariant - everyone will agree it. That does not make your speed invariant, merely your measurement of speed relative to the medium.

Sure, the wavelength is frame invariant. However, as I said, neither the frequency nor wavespeed is frame invariant. Thus your measure of frequency simply gives you your speed relative to the medium (assuming you know the speed of sound relative to the medium in order to subtract it out).

Do you understand that wave speed is frame variant? Because that seems to me to be the bit that you keep missing.

 

[Dale]

Very please, read the page two few sentences — Galilean Transformation of Wave Velocity. Do you anderstand which is means 'invariant'?

As I already said, physics is described by the Lorentz transform, not the Galilean transform. Wavelength is not an invariant. This has been well known now for more than 100 years. Equation 1 in that paper has been known to be incomplete for that same period.

 

[frostysh]

Wind does not have a wavelength.

And that is the reason!

I think you don't understand my point.

I just distracted by the nonsense which is typing the other users, or at least I think it is nonsense... So maybe.

Measuring the speed of the wind simply tells you your speed relative to the medium, whether you regard yourself or the medium or both as moving. That measurement is invariant - everyone will agree it. That does not make your speed invariant, merely your measurement of speed relative to the medium.

The problem the length is not the speed, the wavelength.

Sure, the wavelength is frame invariant. However, as I said, neither the frequency nor wavespeed is frame invariant.

Okay, let's measure the wavespeed, in my frist post it's $\large \left(c + v \right)$.

Thus your measure of frequency simply gives you your speed relative to the medium (assuming you know the speed of sound relative to the medium in order to subtract it out).

Of course.

Do you understand that wave speed is frame variant? Because that seems to me to be the bit that you keep missing.

Yes, that thing is an invariant (I have speciall y not named it by a single symbol), but if this thing $\large \left(c + v \right)$ related to the movement of the source of the waves corresponding to the medium (not vice versa) this very relative speed which you called 'wave speed' producing a very not relative in the inertial frames wavelength, by measuring this wavelength, and knowing the wavelength of the rest case (the very property of the medium), we can distinguish where is the movement, in observer or in the source. This is logic of mine, simple as that.

 

[Ibix]

we can distinguish where is the movement, in observer or in the source

No - you can distinguish where there is movement relative to the medium.

 

[frostysh]

As I already said, physics is described by the Lorentz transform, not the Galilean transform. Wavelength is not an invariant. This has been well known now for more than 100 years.

You are literaly cannot read the name of topic, which is called 'classical Doppler effect', the classical mechanics is a complited self-defined theory, Galelean transformation is no need any Lorentz's transformation to describe the the classical casess. So in the name of WHAT you continuously trying to connect Special Relativity there, it is an enigma for myself, with the all respect...

 

[frostysh]

No - you can distinguish where there is movement relative to the medium.

And your medium relative to what? Oh my god... We have closed, defined system: medium, source, observer. On this system we using Galelean transformation, the end. You can imagine it abstractly — expand the medium to the size of the Universe!

 

[Dale]

You are literaly cannot read the name of topic, which is called 'classical Doppler effect', the classical mechanics is a complited self-defined theory, Galelean transformation is no need any Lorentz's transformation to describe the the classical casess. So in the name of WHAT you continuously trying to connect Special Relativity there, it is an enigma for myself, with the all respect...

Well, you say "classical" in the title, but then in the text you use words like "absolute", "event", "invariant", "frames", and "observer" throughout all of your posts, and you never specify $v<c_s<<c$. All of which essentially require answers to be in the context of relativity if they are to be physically correct answers. I don't know how it is possible to address a question in those terms without relativity.

 

[Ibix]

And your medium relative to what

You can detect the motion of the source relative to the medium or the observer relative to the medium. Or you can see it as the motion of the medium relative to the source or the medium relative to the observer.

Get a source and a receiver and set them in motion relative to the medium and record whatever you want to record - wavelengths, frequencies, whatever. Now do the same experiment (same velocities with respect to the medium and everything) in a moving train. You will get the same results, even though the experiment is doing 60mph with respect to the other one.

There is nothing absolute about this experiment. It is only measuring speeds relative to a medium, which may be in motion with respect to other parts of the medium.

 

[Dale]

On another note, if you can measure the wavelength and the frequency and if $c_s$ is known then I think you can make two equations in two unknowns and solve for both the emitter and the absorber’s speed.

My analysis above presumed only measuring the frequency, since that is the usual meaning of the Doppler shift.

 

[frostysh]

Well, you say "classical" in the title, but then in the text you use words like "absolute", "event", "invariant", "frames", and "observer" throughout all of your posts, and you never specify $v<c_s<<c$. All of which essentially require answers to be in the context of relativity if they are to be physically correct answers. I don't know how it is possible to address a question in those terms without relativity.

Grr! What kind of thought lead you to such conclusion? All things you have named is actually have the same meaning in the classical case. I have provided example of the brick which is splinted into two pieces durring free fall, it is an event, in classic and in the SR kinematics. The relativity exist in classical mechanics too! The different inertial frames exists, so the relativity corresponding to this frames exist too... The classical mechanics relativity in the name of holy Newton, Hamilton and Lagrange can be self-sustained, it's no need this 'relative-relativity' things to describe models. And it's working a very well, and this is actually the case where we totally no need non-classical things.

As for myself, I am not even started to restudy my university course of classical mechanics which I have some studies long ago, but indeed it is a very fundamental and a very crucial point in learning of physics!

 

[Ibix]

I am not even started to restudy my university course of classical mechanics which I have some studies long ago

In that case, maybe listen to three of us who are a bit more current on the topic and are saying you have it wrong?

 

[Dale]

What kind of thought lead you to such conclusion?

A couple of decades of experience in discussing such topics.

The language you are using is far more typical of relativity discussions than classical mechanics discussions. I believe that there is a bit of a language barrier here. Your grammar is odd, with for example a lot of usage of “me” where it should be “I”. So the impression may be unintentional, but nonetheless your wording gives the strong impression that you want to discuss relativity. Particularly with the overuse of the word “absolute” towards the beginning of the thread.

In my decades of previous experience discussing these topics I cannot recall ever having someone who asked about “absolute” and “frames” that did not want to discuss relativity. This is a first

 

[frostysh]

You can detect the motion of the source relative to the medium or the observer relative to the medium. Or you can see it as the motion of the medium relative to the source or the medium relative to the observer.

The relations $\large M \longrightarrow S$ and $\large S \longrightarrow M$ is NOT the same. Assymetry, viola, the end of relativity of inertial frames in case of Doppler's effect.

Get a source and a receiver and set them in motion relative to the medium and record whatever you want to record - wavelengths, frequencies, whatever. Now do the same experiment (same velocities with respect to the medium and everything) in a moving train. You will get the same results, even though the experiment is doing 60mph with respect to the other one.

There is nothing absolute about this experiment. It is only measuring speeds relative to a medium, which may be in motion with respect to other parts of the medium.

The ienrial frame of reference is the inertial frame of reference, the changing of wavelength is an invariant in zillion inertial frame of references. We directly see the direction of this changings! And we directly see it in the all frame of references, in the train, in the car, in the Alpha-Centaura, etc, and we can distinguish the motion! Your bias there...

I understand your position, on the other forum I have pointed that in case of imaginary aquarium with medium, but this is not the point.
Do you understand words 'we have only three inertial frame of references' in the whole Universe? It is an abstraction, no trains, no cars, nothing... This is not he same as free falling in the elevator, we are investigating only the very case of Doppler's effect. Nothing else in world is exist. I am not saying that there is exist an ether, or something that can break relativity as the concept, I am using only the particular model.

A couple of decades of experience in discussing such topics.

The language you are using is far more typical of relativity discussions than classical mechanics discussions. I believe that there is a bit of a language barrier here. Your grammar is odd, with for example a lot of usage of “me” where it should be “I”. So the impression may be unintentional, but nonetheless your wording gives the strong impression that you want to discuss relativity. Particularly with the overuse of the word “absolute” towards the beginning of the thread.

Grammar is yes, of course, my bad, I am apologizing, but the point is the Physics. The Lorentz's transformations is not the same Galelean one...

 

[Dale]

The Lorentz's transformations is not the same Galelean one...

Agreed. I always prefer to start with the general formula I cited, and then explicitly simplify it if $v<c_s<<c$. Mathematically that is how you justify shifting from the correct Lorentz transform to the simplified Galilean transform in the regime where they are approximately equal.

 

[Ibix]

Do you understand words 'we have only three inertial frame of references' in the whole Universe?

Those words are meaningless. You can define a frame of reference with the words "I consider the medium to be moving with velocity $\vec v$". There does not have to be anything at rest in a frame to define it. Thus there are always an infinite number of inertial reference frames available - even in your case with a medium (and what's it made of, by the way? Are any of its molecules moving with respect to any of these frames you say are the only ones that exist?) and two objects.

The relations M⟶S\large M \longrightarrow S and S⟶M\large S \longrightarrow M is NOT the same.

I don't understand what you mean by this. My guess would be that you mean "source moving with respect to the medium is not the same as medium moving with respect to the source", but this is trivially false. So I'm not sure what you do mean.

 

[Ibix]

but this is not the point

It is exactly the point.

Edit - to expand on that, I've just shown you (and you agreed) that you are only measuring speeds with respect to a medium, and that there is no violation of Galilean invariance because the two experiments come out the same.

 

[frostysh]

Agreed. I always prefer to start with the general formula I cited, and then explicitly simplify it if $v<c_s<<c$. Mathematically that is how you justify shifting from the correct Lorentz transform to the simplified Galilean transform in the regime where they are approximately equal.

Or we can forgot about uncle Lorentz so we no need transform anything to 'approximately equal' and not typing such things, and just pary for holy Galeleo...

Those words are meaningless. You can define a frame of reference with the words "I consider the medium to be moving with velocity $\vec v$". There does not have to be anything at rest in a frame to define it. Thus there are always an infinite number of inertial reference frames available - even in your case with a medium (and what's it made of, by the way? Are any of its molecules moving with respect to any of these frames you say are the only ones that exist?) and two objects.

And this is the reason why 'switch on' of' Doppler's effect in the model destroying relativity. You se the change of the invariant is invariant, and if we measured invariant wavelentghs it will say to us where the movement to all inertial frame of refencenses tha you named.

I don't understand what you mean by this. My guess would be that you mean "source moving with respect to the medium is not the same as medium moving with respect to the source", but this is trivially false. So I'm not sure what you do mean.

The all holy saints! I need to describe this diagram earlier. Actually, on my current level of understanding this phenomena it is the difference! It is the true! Why source moving with respect to the medium is not the same as medium moving with respect to the source, because the creation of the waves is an event, and those beacuse it is not more general than Galelean relativity! So in the model we just using a very special event which killing relativity, nothing special, nothing fundamental. Hoorey!

On primitive level I have described it by this picture,

as we can see the change of wavelength is the physical, this is an event, as the breaking of a brick. The explanation of the picture in the first post. If you will move the medium instead, no any change in wavelength appear, because interraction is instant and the speed of medium related to source have no any connection to the very position of the 'cores' related to each others, which is an anlogy in respect to some points of model of one-dimension wave.

 

[Dale]

Or we can forgot about uncle Lorentz

Best not since he is generally right.

By the way, I am not sure if you missed this post of mine above:

https://www.physicsforums.com/threa...the-doppler-effect.975325/page-2#post-6212567

 

[Ibix]

The all holy saints!

I get the impression you are trying to imply that I'm stupid for not following your argument. Am I correct?

because the creation of the waves is an event

No it is not. It's an extended period of time.

the change of wavelength is the physical

...and it happens the same whether you regard the source as moving with respect to the medium or the medium with respect to the source. Proof:

Let the source emit waves of period T and speed c. The medium is stationary and the source moves in the same direction as the waves at speed v. When the second wave crest is emitted, the first wave crest has traveled $cT$ and the source has moved $vT$. Thus the wavelength is $(c-v)T$.

Now again, but this time we regard the source as stationary and the medium as moving at speed $-v$ (i.e., we've subtracted $v$ from the speed of both medium and source). When the second wave crest is emitted, the first has traveled $(c-v)T$ and the source has not moved. Thus the wavelength is $(c-v)T$.

No difference.