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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
25763 Points
one year ago
Let n1 and n2 be the no of loops formed in the wires of radii r and 2r respectively.
f1=2ln1μ1T
f2=2ln2μ2T
where μ1 and μ2 are mass per unit lengths of the wires.

Since the welded wire is continuous, f1=f2
n2n1=μ2μ1=π(2r)2πr2=41=
Vikas TU
14149 Points
one year 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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