A small source of sound vibrating frequency 500 Hz is rotated in a circle of radius `(100)/(pi)` cm at a constant angular speed of `5.0` revolutions per second. The speed of sound in air is `330(m)/(s)`.
Q. For half the circle and smaller during the other half for an observer who is at rest at a great distance from the centre of the circle but nearly in the same plane, the minimum `f_(min)` and the maximum `f_(max)` of the range of values of the apparent frequency heard by him will be

Options

A. `f_(min)=455Hz`,`f_(max)=535Hz`
B. `f_(min)=484Hz`,`f_(max)=515Hz`
C. `f_(min)=484Hz`,`f_(max)=500Hz`
D. `f_(min)=500Hz`,`f_(max)=515Hz`

Answer

B

Explanation

Since the observer is in the same plane as the circle, at one instant of time, the source will move directly towards the observer when the apparent frequency will be maximum given by
`f_(max)=((V)/(V-u))500=((330)/(330-u))500`
Now, `u=romega=((100)/(pi))5xx2pixx10^-2(m)/(s)`
`=10(m)/(s)`
`f_(max)=((330)/(330-10))500=(330)/(320)xx500=515Hz`
Similarly, at another instant, the source will move directly away from the observer with velocity `u=10(m)/(s)`. At this instant, the apparent frequency will be minimum given by
`f_(min)=((330)/(330+10))500=(33)/(34)xx500=485Hz`