> Q. A sonometer wire of length $114, cm$ is fixed at both the ends. Where should the two bridges be placed so as to divide the wire into three segments whose fundamental frequencies are in the ratio $1 : 3 : 4$ ? – LIVE ANSWER TODAY

Q. A sonometer wire of length $114, cm$ is fixed at both the ends. Where should the two bridges be placed so as to divide the wire into three segments whose fundamental frequencies are in the ratio $1 : 3 : 4$ ?

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A sonometer wire of length $114, cm$ is fixed at both the ends. Where should the two bridges be placed so as to divide the wire into three segments whose fundamental frequencies are in the ratio $1 : 3 : 4$ ?

Solution:

Total length of the wire, $L = 114, cm$

$n_2: n_2 : n_3 = 1 :3 :4$

Let $L_1, L_2$ and $L_3$ be the lengths of the three

As $n,propto frac{1}{L}$

$therefore L_{1} : L_{2} : L_{3}=frac{1}{1} : frac{1}{3} : frac{1}{4}=12 : 4 : 3$

$therefore L_{1}=72,cmleft(frac{12}{12+4+3}times114right)$

$L_{2}=24,cmleft(frac{4}{19}times114right)$

and $L_{3}=18,cmleft(frac{3}{19}times114right)$

Hence the bridges should be placed at $72, cm$ and $72 + 24 = 96, cm$ from one end. parts

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