1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Doppler effect Formula manipulation

  1. Apr 21, 2016 #1
    1. The problem statement, all variables and given/known data
    I have this Doppler effect formula, but I don't know how it was derived, I can't repeat the process myself to solve for speed of the source, I would really appreciate if someone could mathematicly solve this in steps, thank you very much.

    2. Relevant equations
    [tex]f=f_{s}\frac{v}{v-v_{s}} \Rightarrow v_{s}=\frac{v(f-f_{s})}{f}[/tex]

    3. The attempt at a solution
    I checked and this is the same thing as the equation above, but mine is messy and ugly, I don't know how to prepare "neaty" formulas like the one above, this often confuses me and forces me to do checks whether my formula is right or not.
    [tex]v_{s}=\frac{-f_{s}v}{f}+v[/tex]
     
    Last edited: Apr 21, 2016
  2. jcsd
  3. Apr 21, 2016 #2

    gneill

    User Avatar

    Staff: Mentor

    Show, step by step, what you've tried and where you've become stuck.
     
  4. Apr 21, 2016 #3
    Ok here's how I did it:

    [tex]f=f_{s}\frac{v}{v-v_{s}}[/tex]
    I multiplied this by: [tex](v-v_{s}) \Rightarrow f(v-v_{s})=f_{s}v[/tex]
    Then I divided by F and subtracted v
    [tex]-v_{s}=\frac{f_{s}v}{f}-v[/tex]

    Finally I multiplied by the negative sign, that's my result:
    [tex]v_{s}=\frac{-f_{s}v}{f}+v[/tex]

    I know they both are equal because I checked, but I don't have the skill to make my formula "neat" I often don't understand how people derive their formulas, I hope you know what I mean, I can't transform my formula into one above.
    [tex]\frac{v(f-f_{s})}{f} = \frac{-f_{s}v}{f}+v[/tex]
     
  5. Apr 21, 2016 #4

    gneill

    User Avatar

    Staff: Mentor

    Combine the terms on the RHS with a common denominator.
     
  6. Apr 21, 2016 #5
    Like this?
    [tex]v_{s}=\frac{-f_{s}v}{f}+\frac{vf}{f}[/tex]
    Wait I see where this is going..
    [tex]v_{s}=\frac{-f_{s}v+vf}{f}[/tex]
    [tex]v_{s}=\frac{v(f-f_{s})}{f}[/tex]
    Is this right?
     
  7. Apr 21, 2016 #6

    gneill

    User Avatar

    Staff: Mentor

    Yup.
     
  8. Apr 21, 2016 #7
    Wow thank you.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Doppler effect Formula manipulation
  1. Formula Manipulation (Replies: 7)

  2. Manipulating a formula (Replies: 15)

  3. Manipulate formula (Replies: 19)

Loading...