A sonometer wire of resonating length 90 cm has a fundamental frequency of 400 Hz when kept under some tension. The resonating length of the wire with fundamental frequency of 600 Hz under same tensio

Question

A sonometer wire of resonating length 90 cm has a fundamental frequency of 400 Hz when kept under some tension. The resonating length of the wire with fundamental frequency of 600 Hz under same tension _____ cm .

TestHub · Accepted Answer

​ f 0 ​ = 400 Hz ; v = μ T ​ ​ = constant 2 λ ​ = L ; v = f 0 ​ λ ​ ​ 2 f 0 ​ v ​ = L ⇒ v = 2 Lf 0 ​ L ′ = 2 f ′ v ​ = 2 f ′ 2 Lf 0 ​ ​ = f ′ Lf 0 ​ ​ = 600 90 × 400 ​ = 60 ​

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