A train producing frequency of `640 Hz` is moving towards point `c` with speed `72 km//hr`. A person is sitting `1732 m` from point `c` as shown. Find the frequency heard by person if speed of sound is `330 m//s`.

Explanation

The observer `A` is at rest with respect to the air and the source is travelling at a velocity of `72 km//h` i.e.,
`20 m//s`. As is clear from the figure, the person receives the sound of the whistle in a direction `BA` making an angle `theta` with the track where `tan theta = (1732)/(1000) = sqrt(3)`, i.e. `theta = 60^(@)`. The component of the velocity of the source is approching the person with this component, the frequency heard by the observer is
`upsilon' = (v)/(v - ucostheta) upsilon = (330)/(330 - 10) xx 640 Hz = 660 Hz`.