• Support PF! Buy your school textbooks, materials and every day products Here!

Doppler Effect for light

  • Thread starter Skeptic.
  • Start date
  • #1
5
0

Homework Statement



This isn't strictly a homework problem, but I didn't know where else to post this. I can't get the same derivation as my lecturer for the Doppler effect of light - which is shown in the attached file. If you cannot open this, I re-wrote it further down.

Homework Equations




The Attempt at a Solution


For the part in the red box, I thought one would do this via Taylor expansion, thus I expected the ##\frac{u}{c}## to be squared, i.e fr = fs##(1 \pm \frac{1}{2}\frac{u}{c}^2)(1 \pm \frac{1}{2}\frac{u}{c}^2)##. I can't see why this wouldn't be the case. Could someone please tell me why I'm wrong?

(In case you cannot open the file, my lecture notes say fr = fs##(1 \pm \frac{u}{c})^\frac{1}{2} (1 \pm \frac{u}{c})^\frac{-1}{2}##=##(1 \pm \frac{1}{2}\frac{u}{c})(1 \pm \frac{1}{2}\frac{u}{c})##)
 

Attachments

Answers and Replies

  • #2
TSny
Homework Helper
Gold Member
12,537
2,955
McClaurin series of (1+x)1/2 = 1 + (1/2) x + .... Note that x is not squared in the second term of the right side.
 

Related Threads on Doppler Effect for light

Replies
2
Views
502
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
4
Views
2K
Replies
2
Views
2K
Replies
1
Views
1K
  • Last Post
Replies
3
Views
763
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
1
Views
758
  • Last Post
Replies
1
Views
670
  • Last Post
Replies
6
Views
3K
Top