Question:
A string of length ℓ is fixed at both ends. It is vibrating in its 3rd overtone with maximum amplitude a. The amplitude at a distance ℓ/6 from one end is:
A string of length ℓ is fixed at both ends. It is vibrating in its 3rd overtone with maximum amplitude a. The amplitude at a distance ℓ/6 from one end is:
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Amplitude is zero at nodes in standing waves.
Updated On: Mar 20, 2026
- \(a\)
- \(0\)
- \(\dfrac{\sqrt{3}a}{2}\)
- (a)/(2)
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The Correct Option is B
Solution and Explanation
Step 1: 3rd overtone = 4ᵗh harmonic.
Step 2: Nodes occur at: x = 0, (ℓ)/(4), (ℓ)/(2), (3ℓ)/(4), ℓ
Step 3: Since ℓ/6 lies very close to a node, amplitude is zero.
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