Relativistic Doppler effect (for sound?)

[one_raven]

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).

 

[one_raven]

99 views and no replies?
Does that mean it is that stupid of a question, or no one has wanted to read the link?

 

[pmb_phy]

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

(1+d)^n \approx 1+nd

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

 

[robphy]

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.