Question

A turning fork of frequency 340Hz is vibrated just above a cylindrical tube of height 1.2m. If water is slowly poured into the tube, at what maximum height will resonance occur.

[speed of sound in air = 340ms-1]

Answer 1

In a closed tube, the resonance occurs at the following points from the opened top of the tube:

$$L_1=\frac{v}{4f}=0.25\text{ m},\\ L_2=\frac{3v}{4f}=0.75\text{ m},\\ L_3=\frac{5v}{4f}=1.25\text{ m}.\\$$

But the actual (effective) length of the tube is 1.2 m. Therefore, the resonance will occur at

$$d=L-L_2=1.2-0.75=0.45\text{ m}.$$