Question

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

• A. 350.5 m/sec
• B. 335.5 m/sec
• C. 346.5 m/sec
• D. none of these

Answer 1

The correct option is C 346.5 m/sec

Length of first organ pipe is $l_1=0.75m$

Length of second organ pipe is $l_2=0.77m$

For first closed organ pipe is, $n_1=\frac{v}{4l_1}=\frac{v}{4\times 0.75}=\frac{v}{3}.........\left(1\right)$

For second closed organ pipe is, $n_2=\frac{v}{4l_2}=\frac{v}{3.08}......\left(2\right)$

Beats produced $=3$

So,

$n_1-n_2=3$

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

$v\left(\frac{3.08-3}{3\times 3.08}\right)=3$

$v\left(\frac{1.08}{9.24}\right)=3$

$v=\frac{27.72}{0.08}=346.5m/s$