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

Frequency of circular motion of the source `=omega/(2pi)=(10)/(2pi)=5/pi s^(-1)`. This frequency is the same that of the detector. The detector will record maximum sound when the source moves from to and the detector moves from D to B, i.e., when the source and the detector approach each other. Then, `v=(V+V_(l))/(V-V_(s)) v, V_(l)` is negative as the detector moves opposite to the direction of sound.
`v. =(V+V_(l))/(V-V_(s))v`
`V_(s)=r omega =3 xx 10=30ms^(-1)`
`V_(l)=a xx 2pi xx "frequency of SHM"`
`=6 xx 2pi xx 5/pi =60ms^(-1)`
Maximum sound heard =v.= `((330+60)/(330-30))340=442Hz`.
Minimum sound is heard when the source moves from A to E and the detector moves from B to D i.e, when the source and the detector recede from each other.
Minimum frequency `=(V-V_(l).)/(V+V_(s))v," as "V_(s)` is negative.
`=((330-60)/(330+30))340=255Hz`.