Question

A closed organ pipe can vibrate at a minimum frequency of 500 Hz. Find the length of the tube. Speed of sound in air = $340m{s}^{-1}$.

• A. 8.5 cm
• B. 17 cm
• C. 34 cm
• D. None of these

Answer 1

The correct option is B

17 cm

Particle at closed end won't move. There will be lot of variation in pressure so there will be pressure antinode at closed end, whereas particle is free to move at open end so there will be displacement antinode but pressure node.
Let's generalize and write formula
$f=(2n+1)\frac{v}{4l}$
Given $f=500Hz$
$v=340$ $\frac{m}{s}$
Now n = 0 as minimum frequency of fundamental frequency.
$f=\frac{v}{4l}$
$\Rightarrow f_{min}=\frac{340}{4\times l}$
$l=\frac{340}{4\times 500}=0.17m=17cm$