The length of a sonometer wire ' AB ' is 110 cm . Where should the two bridges be placed from end ' A ' to divide the wire in three segments whose fundamental frequencies are in the ratio 1: 2: 3 ?

Step-by-step solution

aligned & L ₁+ L ₂+ L ₃=110 ~cm and & n ₁ ~L ₁= n ₂ ~L ₂= n ₃ ~L ₃ & Required condition, n ₁: n ₂: n ₃:: 1: 2: 3 aligned array ll & n₁ n₂ = 1 2 = L₂ L₁ L₂= L₁ 2 and & n₁ n₃ = 1 3 = L₃ L₁ L₃= L₁ 3 & L₁+ L₁ 2 + L₁ 3 =110 & L₁=60 ~cm ; L₂=30 ~cm , L₃=20 ~cm array The two bridges should be kept at 60 cm and 60+30=90 ~cm .