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

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 ? (A) At 36 cm and 84 cm from one end (B) At 24 cm and 72 cm from one end (C) At 48 cm and 96 cm from one end (D) At 72 cm and 96 cm from one end

Tardigrade Admin · Accepted Answer

Total length of the wire, L = 114 cm n2: n2: n3 = 1 :3 :4 Let L1, L2 and L3 be the lengths of the three As n propto (1/L) ∴ L1: L2: L3=(1/1): (1/3): (1/4)=12: 4: 3 ∴ L1=72 cm((12/12+4+3)×114) L2=24 cm((4/19)×114) and L3=18 cm((3/19)×114) Hence the bridges should be placed at 72 cm and 72 + 24 = 96 cm from one end. parts

Q. A sonometer wire of length 114cm 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 ?

At 36 cm and 84 cm from one end

At 24 cm and 72 cm from one end

At 48 cm and 96 cm from one end

At 72 cm and 96 cm from one end

Q. A sonometer wire of length $114 c m$ 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 $1 : 3 : 4$ ?