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

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`