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

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.

Column-I		Column-II
(a)	$y = Asin \frac{πx}{L} \sin ωt$	(p)	1 antinode, 2 nodes
(b)	$y = Acos \frac{πx}{L} \sin ωt$	(q)	3 nodes, 2 antinodes
(c)	$y = Asin \frac{2 πx}{L} \sin ωt$	(r)	2 antinodes, 1 node
(d)	$y = Acos \frac{2 πx}{L} \sin ωt$	(s)	3 antinodes, 2 nodes

Stationary waves

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Stationary waves

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For a Vibrating stringf=p2lTμ 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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