Question:
A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of 9kg is suspended from the wire. When this mass is replaced by a mass M, the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of M is
A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of 9kg is suspended from the wire. When this mass is replaced by a mass M, the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of M is
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For the same tuning fork and wire:
M ∝ \frac1(number of antinodes)²
Updated On: Mar 19, 2026
- 25kg
- 5kg
- 12.5kg
- 1/25kg
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The Correct Option is A
Solution and Explanation
Step 1: For a sonometer wire:
L = (nλ)/(2)
⟹ λ ∝ (1)/(n)
Step 2: Frequency of tuning fork is constant:
v = fλ ∝ (1)/(n)
Step 3: Wave velocity:
v = √((T)/(μ)) ⟹ T ∝ (1)/(n²)
Step 4: Since T = Mg:
M ∝ (1)/(n²)
(M)/(9) = ((5)/(3))²
⟹ M = 9 × (25)/(9) = 25kg
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