Question

A tuning fork of frequency $340Hz$ is vibrated just above a cylindrical tube of length $120cm$. Water is slowly poured in the tube. If the speed of sound is $340m/s$ then the minimum height of water required for resonance is :

• A. $95cm$
• B. $75cm$
• C. $45cm$
• D. $25cm$

Answer 1

The correct option is C $45cm$

The wavelength of the wave is

$\lambda =\frac{v}{\nu }$

$\lambda =\frac{340}{340}=1m$

Therefore for different resonances, the required lengths of the air column are

$\frac{\lambda }{4}$, $\frac{3\lambda }{4}$, $\frac{5\lambda }{4}$ i.e. $25cm$,$75cm$,$125cm$.

As the length of pipe is$120cm$, the resonance corresponding to $125cm$ is not possible.

So, when the water is slowly poured, the first resonance will occur at length

$75cm$ of air column. Hence, the height of water is

$h=120-75=45cm$.