A source of sound is rotating in the anticlockwise direction on a circle of radius 3 m, with an angular velocity of `10" rad s"^(-1)`, given the frequency of the sound produced is 340 Hz and the velocity of sound is `330"m s"^(-1)`. The maximum frequency heard by the observer in the plane of the circle at a large distance will be

Options

A. 300 Hz
B. 374 Hz
C. 474 Hz
D. none of these

Answer

B

Explanation

The tangential velocity of the source of sound is
`v_s = r omega rArr v_(s) = 3 xx 10"m s"^(-1) rArr v_(s) = 30"m s"^(-1)`
`v_(s) = r omega rArr v_(s) = 3 xx 10"m s"^(-1) rArr v_(s) = 30"m s"^(-1)`
The maximum frequency will be heard when the source is at B (as the distance of AO is large)
The observed frequency
`v_("obs") = (v xx v_("sound") )/( (v_("sound" - v_("source") ))`
`v_("obs") = (340 xx 330)/( (330 - 30) ) rArr v_("obs") = 340 xx (330)/( 300)`
`rArr v_("obs") = 374" Hz".`