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  4. A whistle of frequency 540 Hz rotates in a horizontal circle of radius 2 m at an angular speed of 15 rad / s. The highest frequency heard by a listener at rest with respect to the centre of circle (velocity of sound in air =330 ms -1 )

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Q. A whistle of frequency $540\, Hz$ rotates in a horizontal circle of radius $2\, m$ at an angular speed of $15\, rad / s$. The highest frequency heard by a listener at rest with respect to the centre of circle (velocity of sound in air $=330\, ms ^{-1}$ )

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Solution:

Velocity of source
$v_{s}=r \omega=2 \times 15=30\, m / s$
The highest frequency heard by the stationary listener
$f'=f\left(\frac{v}{v-v_{s}}\right)$
or $f'=540\left(\frac{330}{330-30}\right)=594\, Hz$