A whistle emitting a loud sound of frequency 540 Hz is whirled in a horizontal circle of radius 2 m and at a constant angular speed of `15 rad//s`. The speed of sound is `330 m//s`. The ratio of the highest to the lowest frequency heard by a listener standing at rest at a large distance from the center of the circle is

Options

A. `1.0`
B. `1.1`
C. `1.2`
D. `1.4`

Answer

C

Explanation

`v_(1)andv_(2)` are speeds of whistle.
`|v_(1)|=|v_(2)|=omegar=15xx2=30m//s`
maximum frequency heard
`f_(max)=f[(v)/(v-v_(s))]`
minimum frequency heard
`f_(max)=f[(v)/(v+v_(s))]`
`(f_(max))/(f_(min))=(v+v_(s))/(v-v_(s))=(330+30)/(330-30)=(360)/(300)`
`implies (f_(max))/(f_(min))=1.2`.