The Doppler Effect For EM Waves

[sona1177]

Homework Statement

A star is moving away from Earth at a speed of 2.4 x 10^8 m/s. Light of wavelength 480 nm is emitted by the star. What is the wavelength as measured by an Earth observer?

Homework Equations

fo=fs(1 - vrel/c)

I substracted because they the star is moving away from the earth

fo=frequency observed
fs=frequency of source

I know that c/lambda for wavelength of light = (3.0 x 10^8)/(480 x 10^-9)=6.25 x 10^14

So frequency of observor on Earth = (6.25 x 10^14) (1 - (2.8 x 10^8)/(3.0 x 10^8))

Frequency of source = 4.17 x 10^13

Therefore, velocity of source/frequency of source = wavelength observered = (3.0 x 10^8/4.17 x 10^13)= 7.2 x 10^-6 m

This is wrong the answer is supposed to be 1440 nm. what have i done wrong? thanks!

The Attempt at a Solution

 

[vela]

You're not using the correct formula for the relativistic Doppler shift, which you need to use since you're dealing with light.

 

[sona1177]

You're not using the correct formula for the relativistic Doppler shift, which you need to use since you're dealing with light.

Thanks, I just realize that I can't use the formula I was using since the speed of the star and light are very close. I have to use the longer version. Could you please take a look at my question about antennas? I am very confused . . . and I have an exam today. thanks!