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Doppler effect Formula manipulation

  • Thread starter Trec93
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  • #1
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Homework Statement


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.

Homework Equations


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

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:

Answers and Replies

  • #2
gneill
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Show, step by step, what you've tried and where you've become stuck.
 
  • #3
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Show, step by step, what you've tried and where you've become stuck.
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]
 
  • #4
gneill
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20,792
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Combine the terms on the RHS with a common denominator.
 
  • #5
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Combine the terms on the RHS with a common denominator.
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?
 
  • #6
gneill
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20,792
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Yup.
 
  • #7
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