A sonometer wire when vibrated in full length has frequency n. Now it is divided by the help of bridges into a number of segments of length λ 1 , λ 2 , λ 3 , ...., When vibrated these segments have frequencies n 1 , n 2 , n 3 , .... then the correct relation is:
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From law of length, the frequency of vibrating string is inversely proportional to its length, i.e.,
n ∝ 
or n λ = constant (say k)
or n λ = k or λ = 
The segments of string of length λ 1 , λ 2 , λ 3 ..... have frequencies n 1 , n 2 , n 3 ,....
Total length of string is λ
So, λ = λ 1 + λ 2 + λ 3 + .....
∴ 
or 
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