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

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(4) At 72 cm and 96 cm from one end. For a fixed tension and wire, f∝1/L, so the lengths are in the ratio 1:1/3:1/4=12:4:3. The total is 19 parts over 114 cm, so one part is 6 cm and the segments are 72 cm, 24 cm and 18 cm. The bridges therefore sit 72 cm and 72+24=96 cm from that end.

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

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