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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