A small source of sound vibrating at a frequency 500Hz is rotated along a circle of radius `(100)/(pi) cm` at a constant angular speed of 5 revolutions per second. The minimum and maximum frequency of the sound observed by a listener situation in the plane of the circle is (speed of sound is `332 ms^(-1)`)

Options

A. 338.5 Hz, 6125 Hz
B. 485.4 Hz, 535.6 Hz
C. 435.3Hz, 565.6 Hz
D. 485.4 Hz, 515.5 Hz

Answer

D

Explanation

The linear velocity of whistle, `v_(s) = r omega`
`v_(s) =(100)/(pi) cm xx 5` rev/s
`=(1)/(pi) m xx 2pi xx 5 " rev"//s = 10 m//s`
When whistle approaches the listener, then the frequency of sound heard will be maximum and minimum.
`n_("max") = n ((v)/(v-v_(s))) = 500 xx (332)/(322) = 515.5Hz`
`n_("min") = n((v)/(v + v_(s))) = 500 xx (332)/(342) = 485.4Hz`