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 kin 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.

Explanation

`u = 72 km//hr = 20 m//s, cos theta = 12//13`
Frequency received at `O`, due to `S_(1)`
`f_(1) = f((v)/(v - u cos theta)) = 500((340)/(340 - (20 xx 12)/(13))) = 529 Hz`
Frequency received at `O`, due to `S_(2)`
`f_(2) = f((v)/(v + u cos theta)) = 500((340)/(340 - (20 xx 12)/(13))) = 474 Hz`