Relativistic Doppler effect (for sound?)

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Discussion Overview

The discussion centers around the differences and similarities between the classic Doppler Effect and the Relativistic Doppler Effect, particularly in the context of sound waves. Participants explore the derivation of both formulas and the implications of using the standard Doppler Shift formula at various speeds.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant mentions a paper claiming there is no difference between the classic and relativistic Doppler Effect equations, suggesting that the classic formula is an approximation valid for low speeds of sound but inadequate at higher speeds.
  • Another participant expresses uncertainty about the accuracy of the paper due to their limited math skills and seeks input from others with more advanced knowledge.
  • A different participant notes that the first equation from the linked article did not seem familiar and suggests that applying a specific approximation to the relativistic version would yield a factor of 1/2 in the velocity ratios.
  • Another participant points out that there are unified derivations for the Doppler Effect for both light and sound, but finds these derivations to be more complicated than necessary.
  • This participant also mentions that the diagram from the linked article applies to both light and sound, but emphasizes the importance of considering the scales involved in each case.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the accuracy of the paper discussed, and multiple viewpoints regarding the derivation and application of the Doppler Effect equations remain. There is uncertainty about the familiarity and correctness of the equations presented.

Contextual Notes

Some participants express limitations in their mathematical understanding, which may affect their ability to evaluate the claims made in the article. The discussion also highlights the complexity of deriving the Doppler Effect in different spacetime frameworks.

one_raven
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A while back I was involved in a discussion regarding the difference between the classic Doppler Effect equation and the Relativistic Doppler Effect equation explaining red/blue shift in stars.
I went looking for how to derrive both formulas and came across this interesting article that explains how there is actually no difference between the two.

My math skills are quite lacking, and I would be the wrong person to judge the paper's accuracy.

Accodring to the author, the commonly used formula for standard Doppler Shift is an approximation that is accurate enough for the low speed of sound wave propagation, but fails at higher speeds (presumably due to the exponentially increasing shift, but as some of the math is beyond me, I have just breezed the article so far).

I would very much like to know if it is correct, and was hoping some here (who's math has exceded the High School level) would also find the article interesting enough to read it and share their opinions on its accuracy (and maybe point out where the author went wrong if it is not).
 
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99 views and no replies?
Does that mean it is that stupid of a question, or no one has wanted to read the link?
 
one_raven said:
99 views and no replies?
Does that mean it is that stupid of a question, or no one has wanted to read the link?
I took a look at that page and the first equation (non-relativistic) did not look familiar to me. For slow speeds, if one were to take the relativistic version and apply the approximation

[tex](1+d)^n \approx 1+nd[/tex]

Then I'd expect to see a factor of 1/2 in from of the velocity ratios in both the numerator and denominator.

Sorry I couldn't help more.

Pete
 
I haven't read through the page you linked to.

However, I do know that there are "unified" ways of deriving the Doppler Effect for light (in Minkowski spacetime) and for sound (in Galilean spacetime). (For example http://www.iop.org/EJ/abstract/0031-9120/31/6/014 .) Unfortunately, every unified derivation I've seen seems more complicated than necessary.

The diagram on that page you linked works equally well for light and for sound... of course, when you pay attention to scales, the actual slopes for light and for sound would differ. The functional differences between the two cases shows up when you compare the time-intervals using the appropriate spacetime.
 

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