A sonometer wire of length 114 ~cm is fixed at both the ends. Where should the two bridges be placed so as to divide the wire into three segments whose fundamental frequencies are in the ratio 1: 3: 4 ?

Question

Quantrex Academy · Accepted Answer

Correct answer: D. At 72 ~cm and 96 ~cm from one end

Total length of the wire, L =114 ~cm n ₁: n ₂: n ₃=1: 3: 4 Let L ₁, ~L ₂ and L ₃ be the lengths of the three parts As n 1 ~L aligned & L ₁: L ₂: L ₃= 1 1 : 1 3 : 1 4 =12: 4: 3 & L ₁=72 ~cm ( 12 12+4+3 114 ) & L ₂=24 ~cm ( 4 19 114 ) & and L ₃=18 ~cm ( 3 19 114 ) aligned Hence the bridges should be placed at 72 ~cm and 72+24=96 ~cm from one end.

A sonometer wire of length 114 ~cm is fixed at both the ends. Where should the two bridges be placed so as to divide the wire into three segments whose fundamental frequencies are in the ratio 1: 3: 4 ?

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