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. If the observer moves towards the source with a constant speed of `20(m)/(s)`, along the radial line to the centre, the fractional change in the apparent frequency over the frequency that the source will have if considered at reat at the centre will be

Options

A. `6%`
B. `3%`
C. `2%`
D. `9%`

Answer

A

Explanation

The frequency of the source considered stationary at the centre is `n_0=500Hz` when the observer moves towards the centre with constant speed u, the apparent frequency is
`n_a=((V+u)/(V))500=9330+(20)/(330)xx500=(35)/(33)xx500`
Change in frequency is given by
`n_a-n_0=((35)/(33)xx500-500)=(2xx500)/(33)Hz`
Fractional change of frequency is
`((n_s-n_0)/(n_0))=((2xx500)/(33))xx(1)/(500)`
`=(2)/(33)=0.06`
Hence, percentage change is `6%`