Question

A closed orgain pipe has length ${}^{\prime }{l}^{\prime }$. The air in it is vibrating in $3^{rd}$ overtone with maximum displacement amplitude ${}^{\prime }{a}^{\prime }$. The displacement amplitude at distance $l/7$ from closed end of the pipe is :

• A. 0
• B. a
• C. a / 2
• D. none of these

Answer 1

The correct option is B a

The figure shows a variation of displacement of particles in a closed organ pipe for 3rd overtone.

For third overtone, the length of air column is

$l=\left[2\right(3)+1]\frac{\lambda }{4}$

$l=\frac{7\lambda }{4}$

$\frac{\lambda }{4}=\frac{l}{7}$

Since, at closed end there is a node and an antinode is at distance

$\frac{\lambda }{4}$ from it.

Hence, the amplitude (at P) at a distance $\frac{l}{7}$ from closed end is a.