Two wires of same material of radius ' r ' and ' 2 r ' respectively are welded together end to end. The combination is then used as a sonometer wire under tension ' T '.

Question

Two wires of same material of radius ' r ' and ' 2 r ' respectively are welded together end to end. The combination is then used as a sonometer wire under tension ' T '. The joint is kept midway between the two bridges. The ratio of the number of loops in the wires with that the joint is a node is

TestHub · Accepted Answer

Frequency of vibration will be same for both the segments. If p 1 ​ and p 2 ​ are the number of loops for the wires of radius r and 2 r then we have ​ n = 2 ℓ p 1 ​ ​ π r 2 ρ T ​ ​ = 4 ℓ p 2 ​ ​ π ( 2 r ) 2 ρ T ​ ​ ∴ p 2 ​ p 1 ​ ​ = 2 1 ​ ​

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