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

Answer

A

Explanation

When the observer move towards the source the apparent frequency increases
`n_(1) = ((v + v_(0))/(v))n`…(1)
and when he goes away from the source after crossing the source, the apparent frequency decreases.
`n_(2) = ((v - v_(0))/(v)) n` ...(2)
`:. n_(1) - n_(2) = (n)/(v) [v + v_(0) - v + v_(0)]`
`= (2v_(0)n)/(v)`