A U-tube having uniform cross-section but unequal arm length I_(1)=100 cm and I_(2)=50 cm has same liquid of density rho_(1) filled in it upto a height h=30 cm as shown in figure. Another liquid of density rho_(2)=rho_(1)//2 is poured in arm. A Both liquids are immiscible What length of the second liquid (in cm) should be poured in A so that second overtone of A is in unison with fundamental tone of B. (Neglect end correction)

A U-tube having uniform cross-section but unequal arm length I_(1)=100

1.	A U-tube having uniform cross-section but unequal arm length I_(1)=100 cm and I_(2)=50 cm has same liquid of density rho_(1) filled in it upto a height h=30 cm as shown in figure. Another liquid of density rho_(2)=rho_(1)//2 is poured in arm. A Both liquids are immiscible What length of the second liquid (in cm) should be poured in A so that second overtone of A is in unison with fundamental tone of B. (Neglect end correction)
Answer» Solution :`2x xxrhoxxg=Lxxrho/2 G` Rightarrow`L=4x` FREQUENCY same Rightarrow`LAMBDA`=same `20-x=lambda/4` `70+3x=(5lambda)/4` `70-3x=100-5x` `2x=30,x=15` `L=4x=60` cm

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