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

Sol: $\large n = p \frac{v}{4 L}$ with p = 1, 3, 5, ……

So length of air column in the pipe

$\large L = \frac{p v}{4 n} $

L = 25p cm with p = 1, 3, 5, ….

i.e., L = 25 cm, 75 cm, 125 cm

Now as the tube is 120 cm, so length of air column must be lesser than 120 cm, i.e., it can be only 25 cm or 75 cm. Further if h is the height of water filled in the tube, L + h = 120 cm or h = 120 – L

So h will be minimum when L_{max} =75 cm

(h)_{min} = 120 – 75 = 45 cm.