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Two wires of the same material and same cross section are stretched on a sonometer. One wire is loaded with 1.5 kg and another is loaded with 6 kg. The vibrating length of first wire is 60 cm and its fundamental frequency of vibration is the same as that of the second wire. Calculate vibrating length of the other wire.

 

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Given : m1 = m2 = m, L1 = 60 cm = 0.6 m, T1 = 1.5 kg=14.7 N, T2 =6 kg=58.8 N

n1 = 12L1T1m and  n2 = 12L2T2m

But n= n2

12L1T1m  = 12L2T2m

L2 = T2T1×L1  = 58.814.7×0.6= 1.2 m

The vibrating length of the second wire is 1.2 m.

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