Two electric trains run at the same speed of `72 km h^-1` along the same track and in the same direction with a separation of 2.4 km between them. The two trains simultaneously sound brief whistles. A person is situated at a perpendicular distance of 500 m from the track and is equidistant from the two trains at the instant of the whistling. If both the whistles were at 500 Hz and the speed of sound in air is `340 m s^-1`, find the frequencies heard by the person.

Answer

B, D

Explanation

The person will receive dthe soundin the directions BA and CA making a angle theta with the track.
Here `theta=tan^-1(0.5/2.4)=22^@`
So the velocity of the souce will be `vcostheta` when heard by the observer.
so the apparent frequency received by the man from train B
`f^1=((340+00)/(340-vcos22^@))500`
`=529Hz`
And the apparent frequency heard by the man from Train C,
`f^11=((340+0+0)/(340+vcos22^@))xx500`
`=476Hz