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 continuous sound wave of frequency `340 Hz`, Find the maximum and the minimum frequencies recorded by the detector.

Explanation

Speed of source,
`v_S=romega=3xx10=30(m)/(s)`
Maximum speed of detector,
`v_(max)=v_d=Aomega'=A2pif'=6xx2pixx(5)/(pi)=60(m)/(s)`
The speed of sound is `v=330(m)/(s)`
The frequency recorded by detector is maximum when source and detector approach each other (i.e., source at F and detector at C after times `(3T)/(4)`, and `(3T)/(4)`, respectively, T and `T'` being time periods of source and detector). Then maximum frequency is given by
`n_(max)=(v+v_d)/(v-v_S)n`
`=(330+60)/(330-30)xx340=(390)/(300)xx340=442Hz`
The frequency recorded by detector is minimum when source and detector recede from each other (i.e., source at E and detector at C after time `(T)/(4)`) , so that the minimum frequency is
`n_(min)=(v-v_d)/(v+v_S)n`
`=(330-60)/(330+30)xx340=(270)/(360)xx340=255Hz`