Question

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

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

Answer 1

Answer: (A)

Using relation $v=n\lambda$
$\lambda =\frac{v}{n}=\frac{340}{340}=1m$
If length of resonance columns are $l_1,l_2$ and $l_3$, then $l_1=\frac{\lambda }{4}=\frac{1}{4}m=25cm$ (for first resonance)
$l_2=3\frac{\lambda }{4}=\frac{3}{4}m=75cm$
(for second resonance)
$l_3=\frac{5\lambda }{4}=\frac{5}{4}m=125cm$
(for third resonance)
This case of third resonance is impossible because total length of the tube is $120cm$. So, minimum height of water
$=120-75=45cm$