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The length of the wire between two ends of a sonometer is 100 cm. What should be the positions of two bridges below the wire so that the three segments of the wire have their fundamental frequencies in the ratio of 1 : 3 : 5?
- 1500/23 cm, 2000/23 cm
- 1500/23 cm, 500/23 cm
- 1500/23 cm, 300/23 cm
- 300/23 cm, 1500/23 cm
Correct answer: 1500/23 cm, 2000/23 cm
Solution
The wire is divided into three segments with lengths proportional to the inverse of the fundamental frequency ratio (1:3:5). The total length is 100 cm, so the segments are 50/23 cm, 150/23 cm, and 250/23 cm. The positions of the bridges are at 1500/23 cm and 2000/23 cm from one end.
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