Where Did I Go Wrong in My Doppler Effect Calculation?

[dido525]

Homework Statement

A stationary detector measures the frequency of a sound source that first moves at constant velocity directly toward the detector and then (after passing the detector) directly away from it. The emitted frequency is f.

During the approach the detected frequency is f'app and during the recession it is f'rec. If ( f'app - f'rec)/f = 0.741, what is the ratio vs /v of the speed of the source to the speed of sound?

Homework Equations

f ( f'app - f'rec)/f = 0.741

f'app=f(v/(v+v(s) )

f'rec=f(v/(v-v(s))

The Attempt at a Solution

(f(v/(v+v(s)))-(f(v/(v-v(s)))/(f) =0.741

(v/(v+v(s)))-(v/(v-v(s)))=0.741

(v(v-v(s))-v(v+v(s)))/((v+v(s))(v-v(s)) =0.741

(-2V*V(s))/((v+v(s))(v-v(s)) =0.741

Now I can't make the equation in the form V(s)/V no matter what I do. Where did I go wrong in this question?

 

[haruspex]

Homework Equations

f ( f'app - f'rec)/f = 0.741

f'app=f(v/(v+v(s) )

f'rec=f(v/(v-v(s))

Those equations would make f'app < f and f'rec > f. Does that seem right? Even swapping them, there's a problem with the v = vs case. Check with http://en.wikipedia.org/wiki/Doppler_effect.

 

[dido525]

Never mind. I got the right answer. Assume v=1 . Solve for v(s) . You have your ratio.