Speed of the observer??

Question

I When an observer moves towards a stationary source with a certain velocity, he observes an apparent frequency.When he moves away from the source with same velocity, the observed frequency is 0.8 f . If the velocity of sound isv  then the speed of the observer is 

Answer 1

Let the original frequency of the source be f

from doppler effect

When it moves towards stationary source

f₁ = f₀ \((\cfrac{v_{source}+v_{observer}}{v_{source}})\)

f = f₀ \((\cfrac{v_{source}+v_{observer}}{v_{source}})\)  ...(1)

When it moves away from stationary source

f₂ = f₀ \((\cfrac{v_{source}-v_{observer}}{v_{source}})\)

0.8f = f₀ \((\cfrac{v_{source}-v_{observer}}{v_{source}})\)  ...(2)

Dividing equation (1) and (2) we get

f/0.8 f = \(\cfrac{v_{source}+v_{observer}}{v_{source}-v_{observer}}\)

10/8 = \(\cfrac{v+v_{observer}}{v-v_{observer}}\)

10v - 10 v_observer = 8v + 8 v_observer

2v = 18 v_observer

v_observer = 2/18 v

where v = velocity of sound

v_observer = velocity of observer