In a resonance column first and second resonance are obtained at depths 24 ~cm and 78 ~cm the third resonance will be obtained at depth.

Step-by-step solution

Given, first resonance column at depth, l₁=24 ~cm Second resonance column at depth, l₂=78 ~cm Third resonance column at depths, l₃= ? As aligned & l₁+x= 4 =24 (i) & l₂+x= 3 4 =78 (ii) & l₃+x= 5 4 (iii) aligned From Eqs. (i) and (ii), x= l₂-3 l₁ 2 = 78-3(24) 2 =3 (iv) From Eqs. (iii) and (i), l₃+x l₁+x =5 l₃=5 l₁+5 x-x=5 l₁+4 x Substituting l₁ and x value, we get l₃=5(24)+4(3) l₃=132 ~cm .