Question

The lengths of two closed organ pipes are $0.750m$ and $0.770m$. If they are sounded together, $3$ beats per second are produced. The velocity. of sound will be :

• A. 330.5 m/sec
• B. 340.5 m/sec
• C. 346.5 m/sec
• D. None of these

Answer 1

Answer: (C)

For first closed organ pipe
$n_1=\frac{v}{4l_1}=\frac{v}{4\times 0.75}$
For second closed organ pipe
$n_2=\frac{v}{4l_2}=\frac{v}{4\times 0.77}$
But $n_1-n_2=3$
$\frac{v}{4\times 0.75}-\frac{v}{4\times 0.77}=3$
$\frac{v}{3}-\frac{v}{3.08}=3$
$v\left(\frac{3.08-3}{3\times 3.08}\right)=3$
$\Rightarrow v=\frac{3\times 3\times 3.08}{0.08}$
$=346.5m/sec$