A road passes at some distance from a standing man. A truck is coming on the road with some acceleration. The truck driver blows a whistle of frequency `500 Hz` when the line joining the truck and the man makes an angle `theta` with the road. The man hears a note having a note having a frequency of `600 Hz` when the truck is closest to him. Also the speed of truck has git doubled during this time. Find the value of `'theta'`.

Answer

`theta = 60^(@)`

Explanation

Let the truck velocity be `v_(S)`
then, `600 = ((v)/(v - v_(S)costheta))500`……(i)
As `2v_(S) = v_(S) + at`
`v_(S) = at" …"(ii)`

where `'a'` is accelertion.
As `vt = (l)/(sintheta)`
where `v` is velocity is sound.
Also, `lcottheta = v_(S) t + (1)/(2)at^(2)`
`(lcostheta)/(sintheta) = (3)/(2)at^(2)` (from eqn `(ii)`)
`(lcostheta)/(sintheta) = (3)/(2)a((l)/(vsintheta))^(2)`
`(al)/(v) = ((2)/(3)sinthetacostheta)v` ......(iii)
from `(i)`
`(6)/(5) = (v)/(v - atcostheta) = (v)/(v - (al)/(vsintheta)costheta)`
Put `(al)/(v)` from `(iii)`
`:. theta = 60^(@)`