# Sound Doppler shift asymmetry confusion

1. Jul 11, 2014

### 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?

Last edited: Jul 11, 2014
2. Jul 11, 2014

### 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.

3. Jul 11, 2014

### A.T.

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

4. Jul 11, 2014

### user3

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) ?

Last edited: Jul 11, 2014
5. Jul 11, 2014

### 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.

6. Jul 11, 2014

### 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.

7. Jul 11, 2014

### A.T.

- 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?

8. Jul 11, 2014

### user3

Thank you all.

9. Mar 9, 2015

### Patrick McCabe

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?

10. Mar 9, 2015

### A.T.

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

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

Last edited: Mar 9, 2015
11. Mar 9, 2015

### 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?

12. Mar 9, 2015

### A.T.

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

13. Mar 9, 2015

### 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.

14. Mar 9, 2015

### 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?

15. Mar 9, 2015

### Staff: Mentor

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

16. Mar 9, 2015

### 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.

17. Mar 9, 2015

### Staff: Mentor

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

18. Mar 9, 2015

### Patrick McCabe

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.

19. Mar 9, 2015

### Staff: Mentor

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.

Last edited: Mar 9, 2015
20. Mar 9, 2015

### A.T.

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.