Question

A tuning fork having a frequency of $\text{170 Hz}$ is vibrating just above a cylindrical tube. The height of the tube is $\text{110 cm}$ . Water is slowly poured in it. What is the minimum height (in $\text{cm}$ ) of water column required for resonance to occur? (Velocity of sound in air = ${\text{340 m s}}^{-1}$ )

Answer 1

Answer: 60

$\lambda =2m$
Resonance will occur at $\frac{\lambda }{4},\frac{3\lambda }{4},\frac{5\lambda }{4}$
$\Rightarrow 50,150,250cm$
Minimum height of water $=110-\frac{\lambda }{4}=110-50=60cm$