Question

The lengths of two closed organ pipes are $0.750 \,m$ and $0.770 \,m$. 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
$n_{1}=\frac{v}{4 l_{1}}=\frac{v}{4 \times 0.75}$
For second closed organ pipe
$n_{2}=\frac{v}{4 l_{2}}=\frac{v}{4 \times 0.77}$
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} $
$=346.5\, m / sec$