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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The frequency of vibration of a string 
Also number of loops = Number of antinodes.
Hence, with 5 antinodes and hanging mass of 9 kg.
We have p = 5 and T = 9g ⇒ ⇒ 
With 3 antinodes and hanging mass M
We have p = 3 and T = Mg ⇒ ⇒ 
n 1 = n 2 ⇒ ⇒ 
⇒ ⇒ 
kg.
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