Question

In a long cylindrical tube, an air-column is constructed by fitting a movable piston. A tuning fork of frequency $416Hz$ sends longitudinal sound waves. Consider the speed of sound in the air as $333m/s$. It is observed that the air-column in the tube vibrates in its fundamental frequency. How far from the open end should the piston be in this situation?

• A. $10cm$
• B. $20cm$
• C. $30cm$
• D. $40cm$

Answer 1

The correct option is B $20cm$

At the piston end, pressure-antinode will be formed. At the open end, there will be a pressure node.

The length of the tube should be $\frac{\lambda }{4}$.

From, $\lambda =\frac{Speed}{Frequency}=\frac{u}{\nu }=\frac{333}{416}=0.8m$

Length of the tube is:

$L=\frac{\lambda }{4}$

$\Rightarrow L=\frac{0.8}{4}=0.2m$

$=20cm$