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 ... $cm$ ? (speed of sound in air $= 340\, m/s$)
AIIMS 2009, Medium
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We have $v=v \lambda$
or $\lambda=\frac{\mathrm{v}}{\mathrm{v}}=\frac{340 \mathrm{m} / \mathrm{s}}{340 \mathrm{Hz}}=1 \mathrm{m}$
First resonating length,
$l_{1}=\frac{\lambda}{4}=\frac{1}{4} \mathrm{m}=25 \mathrm{cm}$
second resonating length,
$l_{2}=\frac{3 \lambda}{4}=\frac{3 \times 1 \mathrm{m}}{4}=75 \mathrm{cm}$
Third resonating length,
$l_{3}=\frac{5 \lambda}{4}=\frac{5 \times 1 \mathrm{m}}{4}=125 \mathrm{cm}$
So third resonance is not possible since the length of the tube is $120 \mathrm{cm}$.
Minimum height of water necessary for resonance $=120-75=45 \mathrm{cm}$
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