Conflicting Transverse Doppler Shift Equations?

[greswd]

http://en.wikipedia.org/wiki/List_of_relativistic_equations#Doppler_shift

and

http://www.physics.umanitoba.ca/~souther/waves02/feb0402/sld011.htm


If you look at the derivation on Wikipedia:

v' = γv


But the one on Uni of Manitoba shows:

f' = f₀(1-β^2)^(1/2) or f' = f/γ



I'm quite confused.

 

[ghwellsjr]

http://en.wikipedia.org/wiki/List_of_relativistic_equations#Doppler_shift

and

http://www.physics.umanitoba.ca/~souther/waves02/feb0402/sld011.htmIf you look at the derivation on Wikipedia:

v' = γvBut the one on Uni of Manitoba shows:

f' = f₀(1-β^2)^(1/2) or f' = f/γ
I'm quite confused.

The first one is for wavelength, the second one is for frequency. Since wavelength is the inverse of frequency, you can change the first one as follows:

v' = γv

1/f' = γ/f

f = γf'

γf' = f

f' = f/γ

 

[greswd]

http://en.wikipedia.org/wiki/List_of_relativistic_equations#Doppler_shift

and

http://www.physics.umanitoba.ca/~souther/waves02/feb0402/sld011.htm


If you look at the derivation on Wikipedia:

v' = γv


But the one on Uni of Manitoba shows:

f' = f₀(1-β^2)^(1/2) or f' = f/γ



I'm quite confused.

The first one is for wavelength, the second one is for frequency. Since wavelength is the inverse of frequency, you can change the first one as follows:

v' = γv

1/f' = γ/f

f = γf'

γf' = f

f' = f/γ

But in the Wiki derivation they use E = hv. Isn't that the same as E = hf?

Which means that v = f as well, not wavelength?

 

[ghwellsjr]

But in the Wiki derivation they use E = hv. Isn't that the same as E = hf?

Which means that v = f as well, not wavelength?

You're probably right.

I was going by the previous equation in the Wiki article which said:

Doppler shift for emitter and observer moving right towards each other (or directly away):

For an emitter moving towards an observer, the shift in the Doppler frequency is greater than one and yet they imply it is less than one. Since they also include "(or directly away)" without further explanation, I guess they expect the reader to know what they are talking about. Consider the source.

BTW: I'm still waiting for a response from you on your Triplet thread.

 

[Samshorn]

http://en.wikipedia.org/wiki/List_of_relativistic_equations#Doppler_shift
and
http://www.physics.umanitoba.ca/~souther/waves02/feb0402/sld011.htm

If you look at the derivation on Wikipedia: v' = γv

But the one on Uni of Manitoba shows: f' = f₀(1-β^2)^(1/2) or f' = f/γ

I'm quite confused.

Both equations are correct, but they refer to two different "transverse" conditions. One equation defines the transverse condition in terms of the rest frame of the emitter, and the other defines the transverse condition in terms of the rest frame of the receiver. These two conditions are different, because of relativistic aberration. Here's a web page that explains this in detail (toward the bottom of the page):

http://www.mathpages.com/home/kmath587/kmath587.htm