Question

A closed organ pipe of length $l$ is vibrating in $3^{rd}$ overtone with amplitude of antinode being ${}^{\prime }{a}^{\prime }$. Amplitude at a distance $\frac{l}{7}$ from the closed end is

• A. $\frac{a}{2}$
• B. $a$
• C. $\frac{\sqrt{3}a}{2}$
• D. $\text{None}$

Answer 1

The correct option is B $a$

$R=a\text{sin}kx$ with $l=(2\times 3+1)\frac{\lambda }{4}$
$\Rightarrow k=2\pi \frac{7}{4l}$
$\therefore R=a\sin 2\pi \frac{7}{4l}.\frac{l}{7}=a\sin \frac{\pi }{2}=a$