The difference between the apparent frequency of a source of sound as perceived by the observer during its approach and recession is 2% of the natural frequency of the source. If the velocity of sound in air is 300 m/s, the velocity of the source is

Options

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

Answer

B

Explanation

`(f_(approach)-f_(recede))/(f)=(trianglef)/(f)=(v)/(v-v_S)-(v)/(v+v_S)`
`(trianglef)/(f)=(v(v+v_S-v+v_S))/(v^2-v_S^2)=(2vv_S)/(v^2-v_S^2)`
But `(trianglef)/(f)xx100=2%`
`implies0.02=(2(300)v_S)/((300)^2-v_S^2)`
`implies0.02=(2(300)v_S)/((300)^2)=(2)/(300)v_S`
`v_S=(0.01)300`
`=3(m)/(s)`