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

Question

Infinity Learn · Accepted Answer

The frequency of vibration of a string $$n=p2lTmAlso$$ number of loops $$=$$ Number of antinodes. Hence, with $$5$$ antinodes and hanging mass of $$9$$ kg.We have p $$=$$ $$5$$ and T $$=$$ $$9g$$ ⇒$$n1=52l9gmWith$$ $$3$$ antinodes and hanging mass M We have p $$=$$ $$3$$ and T $$=$$ Mg ⇒$$n2=32lMgm$$∵$$n1=n2$$⇒$$52l9gm=32lMgm$$⇒$$M=25kg$$

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