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 $$25kg$$ mass, the wire resonates with the same tuning fork forming n antinodes for the same positions of the bridges. The value of n is

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  $$25kg$$ mass, the wire resonates with the same tuning fork forming n antinodes for the same positions of the bridges. The value of  n is

Infinity Learn · Accepted Answer

For a Vibrating $$stringf=p2lT$$μ   $$p=no$$. of loops or no. of of  harmonicsFor the given problem.$$pT=$$ constant   ⇒$$p1T1=p2T2$$  ⇒$$T2T1=p1p2$$    Five antinodes between bridges means $$5$$ loops are formed.​⇒$$25g9g=5p2$$​⇒$$p2=3$$​Thus, $$3$$ loops means three antinodes between bridges.

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