Q164 / 200 · AP EAMCET 2001 · Physics

The sound waves of wavelengths $5 \mathrm{~m}$ and $6 \mathrm{~m}$ formed 30 beats in $3 \mathrm{~s}$. The velocity of sound is

  • Correct answer
    A
    $300 \mathrm{~ms}^{-1}$
  • B
    $310 \mathrm{~ms}^{-1}$
  • C
    $320 \mathrm{~ms}^{-1}$
  • D
    $330 \mathrm{~ms}^{-1}$

Solution

$\lambda_1=5 \mathrm{~m}, \lambda_2=6 \mathrm{~m}$ Frequency of first, $n_1=\frac{v}{\lambda_1}$ Similarly, $n_2=\frac{v}{\lambda_2}$ Number of beats per sec $\left(n_1-n_2\right)=\frac{30}{3}$ $\begin{aligned} \frac{v}{\lambda_1}-\frac{v}{\lambda_2} & =10 \Rightarrow v\left(\frac{1}{\lambda_1}-\frac{1}{\lambda_2}\right)=10 \\ v\left(\frac{1}{5}-\frac{1}{6}\right) & =10 \Rightarrow v\left(\frac{1}{30}\right)=10 \\ v & =300 \mathrm{~m} / \mathrm{s}\end{aligned}$

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

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