Q141 / 160 · TS EAMCET 2007 · Physics

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 $=330 \mathrm{~ms}^{-1}$ )

  • A
    $590 \mathrm{~Hz}$
  • Correct answer
    B
    $594 \mathrm{~Hz}$
  • C
    $598 \mathrm{~Hz}
  • D
    $602 \mathrm{~Hz}$

Solution

Velocity of source $v_s=r \omega=2 \times 15=30 \mathrm{~m} / \mathrm{s}$ The highest frequency heard by the stationary listener $\begin{aligned} f^{\prime} & =f\left(\frac{v}{v-v_s}\right) \\ f^{\prime} & =540\left(\frac{330}{330-30}\right)=594 \mathrm{~Hz}\end{aligned}$

Hence, the correct answer is option: 'B'.

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