Q. An organ pipe $P$ closed at one end vibrates in its first harmonic. Another organ pipe $Q$ open at both ends vibrates in its third harmonic. When both are in resonance with a tuning fork, the ratio of the length of $P$ to that of $Q$ is
A) $1/2$
B) $1/4$
C) $1/6$
D) $1/8$
Explanation
(c) According to question,
1$^{st}$ harmonic of closed organ pipe
$= 3^{rd}$ harmonic of open organ pipe
$\Rightarrow \frac{V}{4L_{c}} = \frac{3V}{2L_{o}} \Rightarrow \frac{L_{c}}{L_{o}} = \frac{1}{6}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.