A source of sound is moving along a circular orbit of radius 3 m with an angular velocity of 10 rad/s. A sound detector located far away from the source is executing linear S.H.M. along the line BD (see Fig. 14.4.13) with an amplitude BC = CD=6m. The frequency of oscillation of the detector is `5//pi` per second. The source is at the point BA when the detector is at the point B. If the source epiits a continuous sound wave of frequency 340 Hz, find the maximum and the minimum frequencies recorded by the detector.

Explanation

Time period of circular motion
`T=(2pi// omega)=(2pi//10)` is same as that of SHM. i.e., `T=(1//f)=(pi//5)`,
so both will complete one periodic motion in same time. Furthermore source is moving on a circle,
its speed `V_(s)=r omega=3xx10=30m//s` and as detector is executing SHM. `V_(D)=omega sqrt(A^(2)-y^(2))=10 sqrt(6^(2)-y^(2))`
i.e, `(V_(D))_(max)=60m//s` when y=0
So `f_(AP)` wil be maximum when both move towards each other.
`f_(max)=f|(V+V_(D))/(V-V_(S))|` with `V_(D)`= max
i.e., the source is at M and detector at C and moving towards B, so
`f_(max)=340[(330+60)/(330-30)]=442Hz`
Similarly `f_(AP)` will be minimum when both are moving away from each other, i.e
`f_(max)=f[(V-V_(D))/(V+V_(s))]` with `V_(D)` = max
i.,e the source is at Nadn detector at C but moving towards D,
`so f_(min) =340[(330+60)/(330+30)]=225Hz`