The difference between the apparent frequency of a sound of soun as perceived by an observer during its approach and recession is `2%` of the natural frequency of the source. If the velocity of sound in air is `300m//s`, the velocity of the source is (It is given that velocity of source `ltlt velocity of sound )

Options

A. `12 m//s`
B. `6 m//s`
C. `1.5 m//s`
D. `3 m//s`

Answer

D

Explanation

Approach:
`{:(rarr v_(s)=u,,larr v_(o) = 0),(overset(*)(S),overset(v)rarr,overset(*)(O)):}`
`f_(1) = f((v)/(v-v_(s))) = f((v)/(v-u))`
Recession:
`{:(rarr v_(o)=0,,larr v_(s) = u),(overset(*)(O),overset(v)larr,overset(*)(S)):}`
`f_(2) = f((v)/(v+v_(s))) = f((v)/(v+u))`
`f_(1) - f_(2) = (2)/(100)f`
`fv ((1)/(v-u) - (1)/(v+u)) = (2f)/(100)`
`v((2u)/(v^(2) - u^(2))) = (2)/(100)`
Since difference in frequencies `f_(1)` and `f_(2)` is small, `u lt lt v`
`(2uv)/(v^(2)) = (2)/(100) rArr u = (v)/(100) = (300)/(100) = 3 m//s`