Two sound waves of lengths $1\text{ m}$ and $1.01\text{ m}$ in a gas produce 10 beats in $3\text{ s}$. The…

Two sound waves of lengths $1\text{ m}$ and $1.01\text{ m}$ in a gas produce 10 beats in $3\text{ s}$. The velocity of sound in gas is
  1. $360\text{ ms}^{-1}$
  2. $300\text{ ms}^{-1}$
  3. $337\text{ ms}^{-1}$
  4. $330\text{ ms}^{-1}$

Solution

Given, $f_1 - f_2 = \frac{10}{3} \Rightarrow \frac{v}{1} - \frac{v}{1.01} = \frac{10}{3}$ $\Rightarrow \quad v = \frac{10 \times 1.01}{3 \times 0.01} = 337 \text{ ms}^{-1}$

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