Sound Doppler shift asymmetry confusion

[user3]

I have come to learn that the Doppler shift equation is asymmetric. That is, the Doppler shift is not the same when source is moving towards the observer or when the observer is moving towards the observer (both with same speed).
I have looked at the derivation of the Doppler shift equation and it says that that's because the relative speed of the observer and the source with respect to the medium is not the same, although their relative speed to each other is. I can see how that affects the math, but I cannot imagine physically why there's a difference(in both cases the observer detects crests faster than normal).

Here's a situation that conveys where I am confused: imagine a blindfolded man who's seated in a remote controlled wheelchair 50 meters from an ambulance. Suppose the ground is so smooth the man wouldn't know it if he started moving, and supposed the man also has an airtight mask on so he wouldn't feel any air brushing on his face. And let us make the man sleep through the acceleration of the chair so he wouldn't know he started moving. The man suddenly hears the siren's frequency rise. Is there any physical difference between the two cases that could enable the man to determine if he's approaching the ambulance or the ambulance is approaching him?

 

[UltrafastPED]

You have eliminated the force of the wind ... and the motion of the wind is the source of the asymmetry, as you have yourself stated.

 

[A.T.]

I cannot imagine physically why there's a difference

Consider the two extreme cases, when velocity of source / reciver relative to the medium approaches the speed of sound.

 

[user3]

Consider the two extreme cases, when velocity of source / reciver relative to the medium approaches the speed of sound.

you mean that what makes the difference is that when the source is moving the wave crest really are compressed, while when the observer is moving he's just moving through them faster(they are not compressed) ?

 

[olivermsun]

Maybe the easiest way to understand the asymmetry is to realize that the sound speed, c, is fixed with respect to the medium. To produce a Dopper UPshift, the source has to move toward the observer, that is, WITH the direction in which the waves propagate. Or, the receiver can move toward the source, and thus AGAINST the propagation of the crests.

 

[user3]

But I already understand that. What I was asking was why the Doppler shift for sound doesn't depend only of the relative velocity only (like the relativistic Doppler shift). But I think I got it now. The speed of the light is same in every frame of reference, while the speed of sound is not.

 

[A.T.]

you that what makes the difference is that when the source is moving the wave crest really are compressed, while when the observer is moving he's just moving through them faster(they are not compressed) ?

Yes, ask yourself:

- How fast must the source move to collapse the distance between the crests to zero?

- How fast must the receiver move through uncompressed crest, to collapse the encounter period to zero?

 

[user3]

Thank you all.

 

[Patrick McCabe]

I asked this question on a new thread, thankfully someone linked me to this one.

I can see that the issue has been addressed, but I do not see an answer.

It is postulated what speed would a source have to move to reduce the wavelength to zero, the speed of sound.

What speed would an observer have to move relative to the source to reduce the wavelength to zero, again the speed of sound.

I have looked and looked for an explanation of this asymmetry. Is there one?

 

[A.T.]

What speed would an observer have to move relative to the source to reduce the wavelength to zero, again the speed of sound.

Nope, think again, and note that the Doppler formulas relate frequencies not wavelengths.

I have looked and looked for an explanation of this asymmetry. Is there one?

The symmetry is broken by the respective speeds of the source & receiver relative to the medium.

 

[Patrick McCabe]

All I'm doing is looking at the diagrams and the derivations being made for the doppler effect.

The medium doesn't even come into these formulas at least not with the sources I have looked at.

I may be dense I truly do not see the difference between the two.

I still don't see where the asymmetry comes in.

My confusion starts with the derivation of the equations. I don't see why there is a difference.

You bring up an interesting point, the medium, but that is not addressed in any derivation I have seen and I have looked at quite a few.

Could you explain the asymmetry or point me in the direction where it is explained?

 

[A.T.]

All I'm doing is looking at the diagrams

Then draw a diagram for a source at rest, and receiver approaching it at the speed of sound.

 

[Patrick McCabe]

None of the formulas I have found have any reference to the medium.

One example is

http://www.school-for-champions.com...ffect_wavelength_derivations.htm#.VP2-Wo7NrPw

In this example I get how the author derives the case of the moving observer.

When the author is deriving the equations for the moving source he substitutes for the period. When he does he uses the period of the source as opposed to the period of the observer which is what it looks like he should use.

I am lost as to why he is doing it different than the other example. There is no explanation for the difference and no mention of the medium.

 

[Patrick McCabe]

Actually as I looked for examples on the web for the asymmetry I found that when one considers the medium through which the wave travels the change is because the values for the speed of the wave changed.

The question I and apparently so many others have asked is why are the formulas setup as asymmetric formula's in the first place. Although this question has been asked it is never answered.

Does someone know why there is asymmetry in the doppler equation?

 

[Dale]

The medium doesn't even come into these formulas at least not with the sources I have looked at.

Here is my favorite derivation which explicitly considers the medium:
http://mathpages.com/rr/s2-04/2-04.htm

 

[Patrick McCabe]

DaleSpam,

Thank you for your post, however the question I am asking, and apparently a lot of other people have asked is where does the presumption of asymmetry come from?

Your post simply presumes there is an asymmetry, there is no discuss why this is so.

It would be logical to presume that whether it is the observer or source that is moving there should not be a difference.

However the equations are made so there is a difference.

It is difficult to understand how moving source equations tend to be derived

I'm not trying to question whether this is correct, I am just asking why different equations are used.

 

[Dale]

Your post simply presumes there is an asymmetry, there is no discuss why this is so.

Did you read the link. It DERIVES the asymmetry. It does not assume it.

 

[Patrick McCabe]

Actually I did read the link, that is why I made the comment.

The link opens to Section 2.4. There are two paragraphs then the doppler equation which includes the asymmetry aspect.

The question I am asking, and others have asked is where does this asymmetry come from. I know these equations have been around over 100 years I am not questioning them. I am simply asking what is the assumption that is being made that makes them asymmetric? As the equation makes no reference to medium, the medium is not the answer to my question.

 

[Dale]

As the equation makes no reference to medium, the medium is not the answer to my question.

Huh?

"a frame of reference in which the medium of signal propagation is assumed to be at rest"
"Let cs denote the speed at which the signal propagates with respect to the medium."
"It's assumed here that va and ve are less than cs"
"Substituting xA = -vetA and xB = vatB into the equation for cs"

EDIT: I think I see what happened. You read the first two paragraphs and stopped. Please read the whole thing, or at least through to the table from the 1938 Ives and Stilwell experiment.

 

[A.T.]

It would be logical to presume that whether it is the observer or source that is moving there should not be a difference.

For two objects in relative motion, there cannot be any difference based on which is assumed at rest. Due to relativity of motion the situation must be symmetrical in the two frames, as both frames are equivalent.

But if the experiment involves a third object, there is no reason to assume symmetry anymore. There is no equivalence, because only one of the two objects can be at rest relative to the third object.

 

[Patrick McCabe]

Well now as there are two response,

Dalespam, yes cs is the speed in the medium, but it does not appear as a variable.

In the equation listed the variables above the division line Va and the variable below the division line Ve is what makes it asymmetric.

I do not doubt it is asymmetric, I just would like to know why. I cannot follow it from any derivation I have found (at least for the moving source or the Ve aspect).As to AT's comment one could presume that they should be the same, however the equations used are clearly asymmetric, which leads to my question.

Why are they asymmetric.

 

[Dale]

Dalespam, yes cs is the speed in the medium, but it does not appear as a variable.

Yes, it does. I don't know how you can say such things. It is blatantly false, look at the equation. It very clearly has cs in it.

You seem to be trolling, although I cannot imagine why you would pick this topic to troll on. The paper I linked to very clearly goes through the exercise of deriving the asymmetry that you mentioned and investigating it in considerable detail. It also very clearly identifies the importance of the medium and the speed wrt the medium at every step of the way.

Your statements to the contrary are obviously and factually false. Furthermore, they are deliberately ignoring the very thing that answers the question that you have repeated over and over. Your question is already answered, clearly and thoroughly!

There is nothing that we can do for you if you are unwilling to even read the material put in front of you and if you are willing to completely misrepresent its content.

 

[A.T.]

Why are they asymmetric.

Why should they be symmetric?

 

[user3]

Imagine that there's air in space, and that on Earth there's a very famous hungry toddler that produces a very loud scream every 1 hour when it's hungry. The screams of the baby are your wave crests. Now, a few planetary systems away there's an alien trying to get some sleep after a long work day (he also just broke up with his gf). The first scream of the baby from Earth wakes the alien up and it gets so mad it hops on its speed-of-sound-fast spaceship and heads for Earth to find the annoying baby. But because the time intervals between the screams of the baby are long enough that the alien can fall asleep on the way, it sleeps enough (they need very little sleep) and decides to let the human baby live.

In an alternative universe the whole thing happens in a different way. The alien is also trying to get some sleep. It hears the first scream and wakes up, but he waits for a minute, doesn't hear anything else and goes back to sleep. Meanwhile (a few months ago from the point of view of Earth {sound takes a few moths to get to the alien's planet}), the baby's mother knew another scream was coming after 1 hour and quickly hopped on her speed-of-sound Mercedes and drove around to calm the baby down. Unfortunately for the alien, the direction she was driving in was towards its planet. She drove for about 10 hours in the same direction, and because she was driving at the speed of sound, none of the screams got far before the next scream was shot. And just as the alien is tucking itself in, its eardrums are punctured by the high pitch 10 consecutive baby screams, and it dies from internal bleeding.

The end.

Moral of the story: if you're the source of sound and you're moving towards the observer, your screams are much closer together than if the observer is moving towards you. Whereas the first alien could sleep between screams, the second alien could not. So the second alien heard a higher frequency than the first alien.