A source is moving across a circle given by the equation `x^(2) + y^(2) = R^(2)` with constant speed `v_(S) = (330pi)/(6sqrt(3))m//s`. In clockwise sense. A detector is stationary at the point `(2R, 0) w.r.t.` the centre of the circle. The frequency emitted by the source is `f_(S)`.
(a) What are the co-ordinates of the source when the detector records the maximum and minimum frequencies. Take speed of sound `v = 330 m//s`.

Answer

`((sqrt(3R))/(2), (R)/(2)) , ((sqrt(3R))/(2), (-R)/(2))
f'_(min)
`=(6sqrt(3))/(6sqrt(3)+pi)f_(S) , f'_(max) = (6sqrt(3))/(6sqrt(3)-pi)f_(S)`

Explanation

Wave emiited at `A` when reach at detector gives maximum apparent frequency during this time source reaches at `E`.
Time taken by sound to reach at `C = (Rsqrt(3))/(v)`
Distance treavelled by the source within this time `= (Rsqrt(3))/(v) (330pi)/(6sqrt(3)) = (55 piR)/(v)`
Hence `theta' = (55piR)/(vR) =(pi)/(6)`
`:.` Angle from horizontal `= 30^(@)`
Hence coordinates `((Rsqrt(3))/(2)+-(R)/(2))`
Also , `n'_(min) = (v)/(v + v_(S))f`
`n'_(max) = (v)/(v - v_(S))f`