If a particle is travelling with a speed of $0.9$ of the speed of sound and is emitting radiations of…

If a particle is travelling with a speed of $0.9$ of the speed of sound and is emitting radiations of frequency $1\text{ kHz}$ and moving towards the observer, what is its apparent frequency (in kHz)?
  1. 1.1
  2. 2.0
  3. 0.1
  4. 10

Solution

Intensity, $I = \frac{1}{2} \rho \omega^2 A^2 v$ or $I \propto \omega^2$ or $I \propto f^2$ $\therefore \frac{I_2}{I_1} = \left(\frac{f_2}{f_1}\right)^2 = \left(\frac{1200}{400}\right)^2 = 9$

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