A car sounding a horn of frequency $1000\text{ Hz}$ passes an observer. The ratio of frequencies of the horn…

A car sounding a horn of frequency $1000\text{ Hz}$ passes an observer. The ratio of frequencies of the horn noted by the observer before and after passing of the car is $11 : 9$. If the speed of sound is $v$, the speed of the car is
  1. $\frac{1}{10} v$
  2. $\frac{1}{2} v$
  3. $\frac{1}{5} v$
  4. $v$

Solution

$f_{\text{Before}} = \left( \frac{v}{v - v_C} \right) \cdot f$ and $f_{\text{After}} = \left( \frac{v}{v + v_C} \right) \cdot f$ $\frac{f_{\text{Before}}}{f_{\text{After}}} = \frac{11}{9} = \left( \frac{v + v_C}{v - v_C} \right) \Rightarrow v_C = \frac{v}{10}$

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