A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of 9 kg 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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12.5 kg

$\frac{1}{25} k g$

25 kg

5 kg

answer is A.

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Detailed Solution

The frequency of vibration of a string $n = \frac{p}{2 l} \sqrt{\frac{T}{m}}$ Also number of loops = Number of antinodes. Hence, with 5 antinodes and hanging mass of 9 kg.

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With 3 antinodes and hanging mass M

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