A train approaching 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 ?

Options

A. 720 Hz
B. 920 Hz
C. 580 Hz
D. 680 Hz

Answer

D

Explanation

The observer A is at rest with respect to the air and the source is travelling at a velocity of 120 km/s, i.e. `((100)/(3))(m)/(s)`. As is clear from the figure, the person receives the sound of the whistle in direction BA making 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 the direction AB is `((100)/(3))xx((3)/(5))(m)/(s)=20(m)/(s)`. As the source is approaching the person with this component, the frequency heard by the observer is `n'=(v)/(v-ucostheta)n=(340)/(340-20)xx640Hz=680Hz`