• # question_answer 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 $=340\,\,m{{s}^{-1}}$) A)  45 cm                         B)  30 cm           C)  40 cm                         D)  25 cm

Correct Answer: A

Solution :

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 ${{l}_{1}}=\frac{\lambda }{4}=\frac{1}{4}\,m=25\,\text{cm}$             (for first resonance) ${{l}_{2}}=3\,\frac{\lambda }{4}=\frac{3}{4}m=75\,\,\text{cm}$ (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 $=120-75=45\,\,\text{cm}$

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