The observer is moving with velocity `'v'_(0)` towards the stationary source of sound and then after crossing moves away from the source with velocity `'v'_(0)`. Assume that the medium through which the sound waves travel is at rest. If v is the velocity of sound and n is the frequency emitted by the source, then the difference between appearent frequencies heard by the observer is

Options

A. `(2nv_(0))/(v)`
B. `(nv_(0))/(v)`
C. `(v)/(2nv_(0))`
D. `(v)/(nv_(0))`

Answer

A

Explanation

When the observer is moving towards the source and source is stationary, then the apparent frequency is given as,
`n' = n ((v+ v_(0))/(v)) "…"(i)`
When the observer is moving away from the source and the source is stationary , then the apparent frequency is given as,
`n'' = - n((v-v_(0))/(v))`
From Eqs. (i) and (ii) , we get
`n' = n'' = (n)/(v) (v' + v_(0) - v+ v_(0))`
`= (2nv_(0))/(v)`