Q177 / 180 · KCET 2013 · Physics

A person with vibrating tuning fork of frequency $338 \mathrm{~Hz}$ is moving towards a vertical wall with a speed of $2 \mathrm{~ms}^{-1}$. Velocity of sound in air is $340 \mathrm{~ms}^{-1}$. The number of beats heard by that person per second is

  • A
    2
  • Correct answer
    B
    4
  • C
    6
  • D
    8

Solution

As the person having tuning fork is moving towards a wall, therefore, $\begin{array}{ll} & v_{s}=v_{0}=2 \mathrm{~m} / \mathrm{s} \text { (given) } \\ \text { So, } & \frac{f^{\prime}}{f}=\frac{v+v_{0}}{v-v_{0}} \\ \Rightarrow & \frac{f^{\prime}-f}{f}=\frac{v+v_{0}-v+v_{0}}{v-v_{0}} \\ \Rightarrow & \frac{\Delta f}{f}=\frac{2 v_{0}}{v-v_{0}} \\ \text { or } & \Delta f=\frac{2 v_{0}}{v-v_{0}} \times f=\frac{2 \times 2 \times 338}{(340-2)}=4\end{array}$

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

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