Question:
A sonometer wire is vibrating in third overtone. There are
A sonometer wire is vibrating in third overtone. There are
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The third overtone is the fourth harmonic, which has four loops.
Updated On: Oct 1, 2026
- 5 nodes and 4 antinodes
- 4 nodes and 5 antinodes
- 4 nodes and 4 antinodes
- 5 nodes and 5 antinodes
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
A sonometer wire is fixed at both ends. Its fundamental has one loop (2 nodes, 1 antinode). The \(n\)th overtone is the \((n+1)\)th harmonic.
Step 2: Detailed Explanation:
Third overtone = 4th harmonic, so the wire vibrates in 4 loops. A wire with 4 loops has 4 antinodes and \(4 + 1 = 5\) nodes (including the two fixed ends).
Step 3: Check the options.
Only option (A) matches 5 nodes and 4 antinodes.
Final Answer:
There are 5 nodes and 4 antinodes, option (A). \[ \boxed{5\text{ nodes},\ 4\text{ antinodes}} \]
A sonometer wire is fixed at both ends. Its fundamental has one loop (2 nodes, 1 antinode). The \(n\)th overtone is the \((n+1)\)th harmonic.
Step 2: Detailed Explanation:
Third overtone = 4th harmonic, so the wire vibrates in 4 loops. A wire with 4 loops has 4 antinodes and \(4 + 1 = 5\) nodes (including the two fixed ends).
Step 3: Check the options.
Only option (A) matches 5 nodes and 4 antinodes.
Final Answer:
There are 5 nodes and 4 antinodes, option (A). \[ \boxed{5\text{ nodes},\ 4\text{ antinodes}} \]
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