A stretched uniform wire of length L under tension T is vibrating with frequency 'n'. A closed pipe of same length is also vibrating with same fundamental frequency 'n'. If T is in

Question

A stretched uniform wire of length L under tension T is vibrating with frequency 'n'. A closed pipe of same length is also vibrating with same fundamental frequency 'n'. If T is increased by 16 N , it is in resonance with 2 nd harmonic of same closed pipe. The initial tension in the wire is

TestHub · Accepted Answer

n = 2 ℓ 1 ​ m T ​ ​ = 4 ℓ v ​ = 2 ℓ 1 ​ n T + 16 ​ ​ = 4 ℓ 3 v ​ T + 16 T ​ ​ = 3 1 ​ T + 16 T ​ = 9 1 ​ 9 T = T + 16 ∴ 8 T = 16 ∴ T = 2 N

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