Question:
The length of a sonometer wire AB is 176 cm. Where should the two bridges be placed from end A to divide the wire into three segments whose fundamental frequencies are in the ratio \(1:2:3\)?
The length of a sonometer wire AB is 176 cm. Where should the two bridges be placed from end A to divide the wire into three segments whose fundamental frequencies are in the ratio \(1:2:3\)?
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For the same wire and tension, frequency is inversely proportional to length.
Updated On: Nov 12, 2026
- 90 cm and 140 cm
- 96 cm and 144 cm
- 92 cm and 142 cm
- 94 cm and 48 cm
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept
For the same wire and tension, \(f\propto\dfrac{1}{l}\). Frequencies in the ratio \(1:2:3\) give lengths in the ratio \(1:\dfrac{1}{2}:\dfrac{1}{3}=6:3:2\).
Step 2: Lengths
The 11 parts make 176 cm, so one part is 16 cm.
\(l_{1}=96\ \text{cm}\), \(l_{2}=48\ \text{cm}\), \(l_{3}=32\ \text{cm}\)
Step 3: Bridge positions
First bridge at 96 cm from A and second at \(96+48=144\) cm from A.
Final Answer:
The bridges should be placed at 96 cm and 144 cm from A. \[ \boxed{\text{(B) }\text{96 cm and 144 cm}} \]
For the same wire and tension, \(f\propto\dfrac{1}{l}\). Frequencies in the ratio \(1:2:3\) give lengths in the ratio \(1:\dfrac{1}{2}:\dfrac{1}{3}=6:3:2\).
Step 2: Lengths
The 11 parts make 176 cm, so one part is 16 cm.
\(l_{1}=96\ \text{cm}\), \(l_{2}=48\ \text{cm}\), \(l_{3}=32\ \text{cm}\)
Step 3: Bridge positions
First bridge at 96 cm from A and second at \(96+48=144\) cm from A.
Final Answer:
The bridges should be placed at 96 cm and 144 cm from A. \[ \boxed{\text{(B) }\text{96 cm and 144 cm}} \]
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