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A tube U–shaped has a uniform cross–section with arm lengths l1 and l2 (l2 < l1). Tube has a liquid of density ρ1 filled to a height h. Another liquid of density ρ2 = ρ1/2 is poured in arm A. Both liquids are immiscible. The length of the second liquid that should be poured in A so that first overtone of A is in unison with fundamental tone of B is

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Correct option: (d)

Explanation: 

Let y be the length of second liquid poured in A. Let the first liquid come down by a level x in arm A and rises by x in arm B. 

Length of air column in arm B is

Since first overtone of arm A is in unison with fundamental tone of B.

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