Question

A closed organ pipe has length ' $\lambda$ '. The air in it is vibrating in $3^{\text {rd }}$ overtone with maximum amplitude ' $a$ '. The amplitude at a distance of $\lambda / 7$ from closed end of the pipe.

• A. a
• B. a/2
• C. $\frac{\sqrt{3}}{2} a$
• D. $\frac{1}{\sqrt{2}} a$

Answer 1

Answer: (A)

The figure shows variation of displacement of particles in a closed organ pipe for $3^{\text {rd }}$ overtone.
For third overtone $l=\frac{7 \lambda}{4}$
or $\lambda=\frac{4 l}{7}$
or $\frac{\lambda}{4}=\frac{l}{7}$

Hence the amplitude at $P$ at a distance $\frac{l}{7}$
from closed end is '$a'$ because there is an antinode at that point.