What is the Doppler shift equation for light?

[criznet]

i've been having a tough time trying to solve the following problem.

A pulsating star has a period of 3 sec as seen from the rest mass frame of the star. What is the period of the star as measured by an observer traveling 2.2e8 m/s with respect to the star?

I assumed that it was simply the doppler shift for light and I found the equation.

f` = f sqrt(1+v^2/c^2) / sqrt(1 - v^2/c^2).

So in changed the given period of 3 sec to frequency by inverting it. plugged in 2.2e8 for v and 3.0e8 for c. I came up with the observed frequency and inverted it for my answer, but it seems that i am incorrect. anyone have insight into this?

dave

 

[NateTG]

IIRC Relativistic Doppler Shift is:
sqrt((1+v/c)/(1-v/c)) = λ'/λ

Hoever, you're looking for time dilation instead, it's the frequency of the pulsar, not the light, that you're interested in.

 

[chroot]

Both you and Nate have the right equation for the relativistic Doppler equation. Here's a page on the relativistic Doppler equation for reference:

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/reldop2.html

What you want is time dilation. When two events occur at the same location in space but at different times, you can very simply relate the time between those events observed by two observers like this:

t₂ = gamma t₁

I get 4.41 seconds.

Be careful when taking this approach: when the two events take place at different space and time coordinates, the expression is more complicated.

- Warren

 

[chroot]

For anyone reading this thread who is unfamiliar with gamma:

gamma = 1 / sqrt(1 - (v/c)^2)

- Warren