Question

A tuning fork of frequency $340\,Hz $ is vibrated just above the tube of $120\,cm $ height. Water is poured slowly in the tube. What is the minimum height of water necessary for the resonance? (speed of sound in air $ =340\,m/s $ )

• A. 45 cm
• B. 30 cm
• C. 40 cm
• D. 25 cm

Answer 1

Answer: (A)

Using relation $v=n \lambda$
$\lambda=\frac{v}{n}=\frac{340}{340}=1\, m$
If length of resonance columns are $l_{1}, l_{2}$ and $l_{3}$, then $l_{1}=\frac{\lambda}{4}=\frac{1}{4} m =25\, cm$ (for first resonance)
$l_{2}=3 \frac{\lambda}{4}=\frac{3}{4} m =75\, cm$
(for second resonance)
$l_{3}=\frac{5 \lambda}{4}=\frac{5}{4} m =125\, cm$
(for third resonance)
This case of third resonance is impossible because total length of the tube is $120\, cm$. So, minimum height of water
$=120-75=45\, cm$