Q. Two closed organ pipes of length $100\ cm$ and $101\ cm$ produce 16 beats in $20\ sec.$ When each pipe is sounded in its fundamental mode calculate the velocity of sound
A) $303\ ms^{- 1}$
B) $332\ ms^{- 1}$
C) $323.2\ ms^{- 1}$
D) $300\ ms^{- 1}$
Explanation
(c) Number of beats per second,
$n = \frac{16}{20} = \frac{4}{5} \Rightarrow n = n_{1} = \frac{v}{4}\left( \frac{1}{l_{1}} - \frac{1}{l_{2}} \right)$
$\Rightarrow \frac{4}{5} = \frac{v}{4}\left( \frac{1}{1} - \frac{1}{1.01} \right) = \frac{0.01v}{4 \times 1.01}$
$v = \frac{16 \times 101}{5} = 323.2\ ms^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.