A train approachign a railway crossing at a speed of `120 kmh^-1` sounds a short whistle at frequency 640 Hz when it is 300 m away from the crossing. The speed of sound in air is `340 ms^-1`. What will be the frequency heard by a person standing on a road perpendicular to the track through the crossing at a distance of 400 m from the crossing ?

Explanation

The observer A is at rest with respect to the air and the source is traveling at a velocity of `120 kmh^-1` i.e., `10/3 ms^-1`. As is clear from the ure, the person receives the sound of the whistle in a direction BA makig an angle theta with the track where `costheta=300/500=3/5`. The component of the velocity of the source (i.e., of the train) along this direction AB is `100/3xx3/5ms^-1=20ms^1`. As the source is approachign the person with this component the frequency heard by the observer is
`v'=v/(v-ucostheta)v=340/(340-20)xx640Hz=680Hz`.