A train is moving with a uniform speed of $33\text{ m/s}$ and an observer is approaching the train with the…

A train is moving with a uniform speed of $33\text{ m/s}$ and an observer is approaching the train with the same speed. If the train blows a whistle of frequency $1000\text{ Hz}$ and the velocity of sound is $333\text{ m/s}$, then the apparent frequency of the sound that the observer hears is [WB JEE 2015]
  1. $1220\text{ Hz}$
  2. $1099\text{ Hz}$
  3. $1110\text{ Hz}$
  4. $1200\text{ Hz}$

Solution

Apparent frequency, $\nu = \left(\frac{v + u_o}{v - u_s}\right) \nu_o = \left(\frac{333 + 33}{333 - 33}\right) \times 1000$ $= \frac{366}{300} \times 1000 = 1220\text{ Hz}$

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