Q170 / 170 · Manipal (MET) 2017 · Physics

A stationary police car sounds a siren with a frequency of 990 Hz . If the speed of sound is $330 \mathrm{~m} / \mathrm{s}$, an observer, driving towards the car with a speed of $33 \mathrm{~m} / \mathrm{s}$, will hear a frequency of

  • A
    891 Hz
  • B
    900 Hz
  • Correct answer
    C
    1089 Hz
  • D
    1100 Hz

Solution

From Doppler's effect the perceived frequency $f^{\prime}$ is given by $f^{\prime}=f\left(\frac{v+v_0}{v}\right)$ Given, $f=990 \mathrm{~Hz}, v=300 \mathrm{~m} / \mathrm{s}, v_0=33 \mathrm{~m} / \mathrm{s}$ $\begin{aligned} \therefore f^{\prime} & =990\left(\frac{330+33}{330}\right) \\ & =990 \times \frac{363}{330}=1089 \mathrm{~Hz} \end{aligned}$

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

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