Question

The length 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. $330.5m/sec$
• B. $340.5m/sec$
• C. $346.5m/sec$
• D. None of these

Answer 1

The correct option is C $346.5m/sec$

For first closed organ pipe $n_1=\frac{V}{44}=\frac{V}{4\times 0.75}=\frac{V}{3.00}=\frac{V}{3}$

For second closed organ pipe $n_2=\frac{V}{{41}_2}=\frac{V}{4\times 0.77}B$

$n_1-n_2=3$

$\frac{V}{3}-\frac{V}{4\times 0.77}=3$

$\frac{V}{3}-\frac{V}{3.08}=3$

$V=\frac{3\times 3\times 3.08}{0.08}=346.5m/sec$.