A whistle of frequency $540 \mathrm{~Hz}$ rotates in a horizontal circle of radius $2 \mathrm{~m}$ at an…
A whistle of frequency $540 \mathrm{~Hz}$ rotates in a horizontal circle of radius $2 \mathrm{~m}$ at an angular speed of $15 \mathrm{rad} / \mathrm{s}$. The highest frequency heard by a listener at rest with respect to the centre of circle (velocity of sound in air $=330 \mathrm{~ms}^{-1}$ )
$590 \mathrm{~Hz}$
$594 \mathrm{~Hz}$
$598 \mathrm{~Hz}
$602 \mathrm{~Hz}$
Solution
Velocity of source
$v_s=r \omega=2 \times 15=30 \mathrm{~m} / \mathrm{s}$
The highest frequency heard by the stationary listener
$\begin{aligned} f^{\prime} & =f\left(\frac{v}{v-v_s}\right) \\ f^{\prime} & =540\left(\frac{330}{330-30}\right)=594 \mathrm{~Hz}\end{aligned}$