# Doppler Shift

1. Feb 24, 2005

### stunner5000pt

uestion is How does the second order term in teh relativistic doppler shift (v/c)^2 compare to the total classical Doppler Shift for the observer receeding away from the source?

now the doppler shift (relativistic) is $$\Delta f = |f_{0} (1-\sqrt{\frac{1-\beta}{1+\beta}})|$$

for the classical shift it is

$$\Delta f = |f_{0} (1-\frac{v_{rel}}{v}-1)| = | f_{0} \frac{v_{rel}}{v}|$$

but i dont see a (v/c)^2 term anywhere? How am i supposed to do this??
refers to part E opf this thread
https://www.physicsforums.com/showthread.php?t=64390

Last edited: Feb 24, 2005
2. Feb 25, 2005

### Staff: Mentor

Do a binomial expansion of:
$$\sqrt{\frac{1-\beta}{1+\beta}} = \frac{\sqrt{1-\beta^2}}{1+\beta}$$

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