Question

An air column is constructed by fitting a movable piston in a long cylindrical tube. Longitudinal waves are sent in the tube by a tuning fork of frequency $416\text{Hz}$. How far from the open end should the piston be so that the air column in the tube may vibrate in its first overtone neglecting the end corrections?
$[$ speed of sound in air $=333\text{m/s}]$

• A. $30\text{cm}$
• B. $45\text{cm}$
• C. $60\text{cm}$
• D. $90\text{cm}$

Answer 1

The correct option is C $60\text{cm}$

We know that for a closed organ pipe, the resonate frequency is given by,
$f=\frac{nv}{4l}$
For first overtone, $n=3$.
$f=\frac{3v}{4l}$
$\Rightarrow 416=\frac{3\times 333}{4\times l}$
[overtone will be equal to the frequency of source]
$\Rightarrow l=\frac{3\times 333}{4\times 416}=0.60\text{m}=60\text{cm}$