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

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