A source of sound is moving along a circular orbit of radius `3 meter` with an angular velocity of `10 rad//s`. A sound detector located far away from the source is executing linear simple harmonic motion along the line `BD` with an amplitude `BC = CD = 6 meters`. the frequency of oscillation of the detector is `(5)/(pi)` per second. the source is at the point `A` when the detector is at the point `B`. if the source emits a continous sound wave of frequency `340 Hz`, find the maximum and the mnimum frequencies recorded by the detector.

Answer

B, C, D

Explanation

`The angular frequency of the detecor = 2piv`
`= 2pi xx (5)/(pi) = 10 rad//s`
The angular frequency of the detector matches with that of the source.

rArr When the detector is at `C` moving `D`, the source is at `A_(1)` moving leftwards. it is in this situation that the frequency heard is minimum
`v' = v[(v - v_(0))/(v - v_(s))] = 340 xx ((340 - 60)/(340 + 30)) = 257 .3 Hz`
Again when the detector is at `C` moving towards `B`, the source is at `A_(3)` moving rightwards. it is in this situation that the frequency heard is maximum.
`v" = v[(v + v_(0))/(v - v_(s))] = 340 xx ((340 + 60)/(340 - 30)) = 438.7 Hz`