A stationary source emits a whistle at a frequency of $200\text{ Hz}$. If the velocity of propagation of…

A stationary source emits a whistle at a frequency of $200\text{ Hz}$. If the velocity of propagation of sound is $340\text{ ms}^{-1}$, then the observed frequency, if the observer is moving away from the source at $25\text{ ms}^{-1}$, will be [MP PMT 2013]
  1. 185 Hz
  2. 215 Hz
  3. 175 Hz
  4. 225 Hz

Solution

As we know, $f' = f\left(\frac{v}{v - v_s}\right)$ Given, $f = 200\text{ Hz}$, $v = 340\text{ ms}^{-1}$, $v_s = 25\text{ ms}^{-1}$ From Doppler's effect, $f' = 200\left(\frac{340}{340 - 25}\right) = \frac{200 \times 340}{315} \Rightarrow f' = 215\text{ Hz}$

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