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Two wires of same material and radii r and 2r respectively are welded together end to end. The combination is used as a sonometer wire and kept under tension T. the welded point is mid-way between the two bridges. When stationary waves are set up in the composite wire, the joint is a node. Then the ratio of the number of loops formed in the thinner to thicker wire is, (a) 2 : 3 (b) 1 : 2 (c) 2 : 1 (d) 5 : 4

Two wires of same material and radii r and 2r respectively are welded together end to end. The combination is used as a sonometer wire and kept under tension T. the welded point is mid-way between the two bridges. When stationary waves are set up in the composite wire, the joint is a node. Then the ratio of the number of loops formed in the thinner to thicker wire is,
(a) 2 : 3
(b) 1 : 2
(c) 2 : 1
(d) 5 : 4

Grade:Upto college level

2 Answers

Arun
25750 Points
3 years ago
Let n1​ and n2​ be the no of loops formed in the wires of radii r and 2r respectively.
f1​=2ln1​​μ1​T​​
f2​=2ln2​​μ2​T​​
where μ1​ and μ2​ are mass per unit lengths of the wires.

Since the welded wire is continuous, f1​=f2​
∴n2​n1​​=μ2​μ1​​​=π(2r)2πr2​​=41​​=
Vikas TU
14149 Points
3 years ago
Dear student
n1/2(l/2)*√T/(πr^2ρ) 
n2/2(l/2)√T/π(4r^2)ρ 
⇒ n1/n2=1/2
Good Luck ….............................

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