A railroad train is travelling at `30(m)/(s)` in still air. The frequency of the note emitted by locomotive whistle is 500 Hz. Speed of sound is `345(m)/(s)`.
Q. What is the frequency of the sound waves heard by a stationary listener in front of the train?

Options

A. `547.6Hz`
B. `690.6Hz`
C. `590.9Hz`
D. `520.3Hz`

Answer

A

Explanation

In front of train: velocity of observer is `V_0=0(m)/(s)` Velocity of source is `V_0=+30(m)/(s)`. The direction from S to O is considered to be the positive direction.
Hence, the apparent frequency is
`f'=f((c-V_0)/(c-V_S))=f((c-0)/(c-30))`
`impliesf'=(500xx345)/(345-30)=547.62Hz`