Q. Two closed organ pipes, when sounded simultaneously gave 4 beats per sec. If longer pipe has a length of $1m.$ Then length of shorter pipe will be, $(v = 300\ m/s)$
A) $185.5\ cm$
B) $94.9\ cm$
C) $90\ cm$
D) $80\ cm$
Explanation
(b) For first pipe $n_{1} = \frac{v}{4l_{1}}$ and for second pipe $n_{2} = \frac{v}{4l_{2}}$
So, number of beats $= n_{2} - n_{1} = 4$
$\Rightarrow 4 = \frac{v}{4}\left( \frac{1}{l_{2}} - \frac{1}{l_{1}} \right) \Rightarrow 16 = 300\left( \frac{1}{l_{2}} - \frac{1}{1} \right) \Rightarrow l_{2} = 94.9\ cm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.